Syllogism

Question 1

PYQ 1.0 marks

Statement: The population of City A is growing at a rate of 10% annually. Conclusions: I. City A will face housing shortages in the future. II. City A has a larger population than City B.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: The statement provides information only about the population growth rate of City A at 10% annually. It gives no data about housing availability, infrastructure capacity, or comparison with City B's population. Therefore, neither conclusion I (housing shortages) nor conclusion II (larger population than City B) logically follows from the given statement. The correct choice is D[2].

Question 2

PYQ 1.0 marks

Statement: The school is closed in May. Conclusions: I. Students are admitted to the school before June. II. The school remains open in June.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: The statement indicates the school is closed specifically in May but provides no information about admission timelines or the school's status in June. Conclusion I assumes admissions occur before June without evidence, and Conclusion II assumes the school is open in June, which is not stated. Thus, neither conclusion logically follows from the statement. Answer: D[2].

Question 3

PYQ 1.0 marks

Statement: The government has launched an initiative to plant 10 million trees across the country. Conclusions: I. The government is concerned about the environment. II. The initiative will completely solve the issue of deforestation.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: Launching a tree-planting initiative directly implies governmental concern for environmental issues like deforestation and climate change, so Conclusion I logically follows. However, planting 10 million trees does not guarantee complete resolution of deforestation, which involves multiple complex factors, so Conclusion II does not follow. Thus, only I follows. Answer: A[2].

Question 4

PYQ 1.0 marks

Statement: Gold prices are rising each day in the market. Conclusions: I. Nobody wears gold nowadays. II. It has become tougher to locate gold deposits.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: Rising gold prices indicate increased market demand or supply constraints but provide no information about consumer wearing habits (Conclusion I) or difficulties in locating gold deposits (Conclusion II). Both conclusions are assumptions not supported by the statement. Therefore, neither follows. Answer: D[5].

Question 5

PYQ 1.0 marks

Statement: Agrima took part in a State-level singing competition and won it. Conclusions: I. Agrima is the best singer in the country. II. Agrima can dance well.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: Winning a state-level competition demonstrates excellence at that level but does not establish Agrima as the national best (Conclusion I), nor does it provide any information about her dancing ability (Conclusion II). Neither conclusion logically follows from the statement. Answer: D[5].

Question 6

PYQ 1.0 marks

Statement: Computer literates have good reasoning ability. Seema can understand the puzzle quickly. Conclusions: I. Seema is computer literate. II. Seema has good reasoning ability.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: The statement establishes that understanding puzzles quickly indicates good reasoning ability, regardless of computer literacy. Thus, Seema has good reasoning ability (II follows). However, good reasoning does not necessarily mean computer literacy (I does not follow, as other factors could contribute). Only II follows. Answer: B[4].

Question 7

PYQ 1.0 marks

Statement: Most students in the class passed the exam. Conclusions: I. All students passed the exam. II. Some students passed the exam.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Both I and II follow D D. Neither I nor II follows

Why: The statement indicates that **most** students passed, which means some (actually more than half) passed, so Conclusion II logically follows. However, 'most' implies not all, so some may have failed, making Conclusion I invalid. Thus, only II follows, corresponding to option B.

Question 8

PYQ 1.0 marks

Statement: The population of City A is growing at a rate of 10% annually. Conclusions: I. City A will face housing shortages in the future. II. City A has a large population compared to other cities.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Both I and II follow D D. Neither I nor II follows

Why: The statement provides only the growth rate of City A's population at 10% annually. Conclusion I assumes housing shortages, but no information is given about housing supply or demand. Conclusion II compares to other cities, but no comparative data is provided. Therefore, neither conclusion logically follows from the statement, making option D correct.

Question 9

PYQ 1.0 marks

Statement: The school announced the commencement of a new academic session starting in June. Conclusions: I. The school is closed in May. II. Students are admitted to the school before June.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Both I and II follow D D. Neither I nor II follows

Why: The announcement of a new session starting in June implies that admissions or preparations occur before June, so Conclusion II follows logically. However, it does not state or imply the school is closed in May; it could be running previous sessions. Thus, only Conclusion II follows, corresponding to option B.

Question 10

PYQ 1.0 marks

Statement: Gold prices are rising each day in the market. Conclusions: I. Nobody wears gold nowadays. II. It has become tougher to locate gold deposits.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Both I and II follow D D. Neither I nor II follows

Why: Rising gold prices indicate increased market demand or other economic factors, but do not imply reduced wearing of gold (I) or difficulty in finding deposits (II). No causal link is provided in the statement for either conclusion. Hence, neither follows, making option D correct.

Question 11

PYQ 1.0 marks

Statement: Computer literates have good reasoning ability. Seema can understand the puzzle quickly. Conclusions: I. Seema is computer literate. II. Seema has good reasoning ability.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Both I and II follow D D. Neither I nor II follows

Why: The statement establishes that understanding puzzles quickly demonstrates good reasoning ability, so II directly follows regardless of computer literacy. However, good reasoning does not necessarily mean computer literacy (I), as other factors could enable puzzle-solving. Thus, only II follows, option B.

Question 12

PYQ 1.0 marks

Statement: The old order changed yielding place to new. Conclusions: I. Change is the law of nature. II. Discard old ideas because they are old.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: The statement describes a natural process of change where old gives way to new, logically supporting I as a general law of nature. Conclusion II introduces a prescriptive action (discard old ideas solely due to age), which is not implied. Therefore, only I follows, option A.

Question 13

PYQ 1.0 marks

Statement: Agrima took part in a State-level singing competition and won it. Conclusions: I. Agrima is the best singer in the country. II. Agrima can dance well.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Both I and II follow D D. Neither I nor II follows

Why: Winning a state-level competition does not extend to national level supremacy (I), as country-level data is absent. No information about dancing skills is given (II). Neither conclusion can be logically derived from the statement, so option D.

Question 14

PYQ 1.0 marks

Below are two statements, followed by two conclusions. Assume both statements are true, even if they contradict common knowledge. Read the conclusions and choose which one logically follows from the two statements, ignoring common knowledge. **Statements**: All students who study regularly pass exams. John studies regularly. **Conclusions**: I. John is a student. II. John will pass the exams.

A A. Only conclusion I follows B B. Only conclusion II follows C C. Either I or II follows D D. Neither I nor II follows

Why: From the first statement, 'All students who study regularly pass exams' implies that anyone who studies regularly must be a student (otherwise the statement wouldn't apply). Since John studies regularly, conclusion I 'John is a student' logically follows. Additionally, since John studies regularly and all such students pass exams, conclusion II 'John will pass the exams' also follows. Thus, both conclusions follow, which corresponds to option E.

Question 15

PYQ 1.0 marks

Statements: All dogs are mammals. Some mammals are pets. Conclusions: I. Some dogs are pets. II. Some pets are dogs.

A A. Only I follows B B. Only II follows C C. Either I or II follows D D. Neither I nor II follows

Why: The first statement establishes 'All dogs are mammals' (universal affirmative). The second is 'Some mammals are pets' (particular affirmative). In syllogistic logic, combining a universal affirmative with a particular affirmative does not guarantee a valid conclusion about dogs and pets, as the 'some mammals' may not overlap with the dogs. No definite connection exists between dogs and pets from the premises. Therefore, neither conclusion I nor II logically follows, corresponding to option D.

Question 16

PYQ 1.0 marks

Statements: No women teacher can play. Some women teachers are athletes. Conclusions: I. Male athletes can play. II. Some athletes can play.

A A. Only I follows B B. Only II follows C C. Either I or II follows D D. Neither I nor II follows

Why: First statement: 'No women teacher can play' (universal negative). Second: 'Some women teachers are athletes' (particular affirmative). Conclusion I 'Male athletes can play' introduces 'male' which is not mentioned in premises, so it does not follow. Conclusion II 'Some athletes can play' cannot be deduced because the athletes mentioned (women teachers) cannot play per the first premise. Since one premise is negative, valid conclusions must be negative, but II is affirmative. Thus, neither follows, option D.

Question 17

PYQ 1.0 marks

Mike finished ahead of Paul. Paul and Brian both finished before Liam. Owen did not finish last. Who was the last to finish?

A A. Owen B B. Brian C C. Paul D D. Liam

Why: Apply process of elimination: 1. Mike finished ahead of Paul, so Mike finished before Paul (Mike cannot be last). 2. Paul and Brian both finished before Liam, so neither Paul nor Brian is last (Liam is after both). 3. Owen did not finish last. All others (Mike, Paul, Brian, Owen) cannot be last, leaving only Liam as the last to finish. This matches option D.

Question 18

PYQ 2.0 marks

Statements: All mangoes are golden in colour. No golden-coloured things are cheap. Conclusions: I. All mangoes are expensive. II. Some golden-coloured mangoes are not cheap.

A A. Only I follows B B. Only II follows C C. Either I or II follows D D. Neither I nor II follows

Why: First premise: All mangoes are golden (universal affirmative). Second: No golden things are cheap (universal negative), equivalent to 'All golden-coloured things are expensive.' Combining: All mangoes are golden, and no golden things are cheap, so the valid conclusion is universal negative: 'No mango is cheap' (or equivalently, 'All mangoes are expensive'). Conclusion I 'All mangoes are expensive' follows this logic. However, II 'Some golden-coloured mangoes are not cheap' is particular and contains the middle term 'golden-coloured' in the conclusion, violating syllogistic rules. The explanation in source indicates II follows via substitution, but strictly, only the universal negative form is valid without middle term in conclusion. Source specifies 'only II follows' as answer, corresponding to option B.

Question 19

PYQ 1.0 marks

Statements: All cats are dogs. All dogs are animals. Conclusions: I. All cats are animals. II. Some animals are dogs. Which conclusion(s) logically follow from the statements?

A Only I follows B Only II follows C Both I and II follow D Neither I nor II follows

Why: Using categorical syllogism logic: Given that all cats are dogs, and all dogs are animals, we can conclude through transitive property that all cats are animals. This makes Conclusion I valid. For Conclusion II, while some animals are indeed dogs (from the second statement), this is not a necessary logical conclusion from the premises. The statements establish that all dogs are animals, but not that some animals must be dogs. Therefore, only Conclusion I logically follows from the given statements.

Question 20

PYQ 1.0 marks

Statements: Some pens are books. No book is a pencil. Conclusions: I. Some pens are not pencils. II. All books are pens. Which conclusion(s) logically follow from the statements?

A Only I follows B Only II follows C Both I and II follow D Neither I nor II follows

Why: Analyzing the syllogism: From 'Some pens are books' and 'No book is a pencil', we can deduce that some pens (those that are books) cannot be pencils, making Conclusion I valid: Some pens are not pencils. However, Conclusion II states 'All books are pens', which directly contradicts the first statement 'Some pens are books'. The first statement does not establish that all books are pens; it only states that some pens are books. Therefore, only Conclusion I logically follows.

Question 21

PYQ 1.0 marks

Statements: All chairs are tables. Some tables are wooden. Conclusions: I. All chairs are wooden. II. Some wooden objects are chairs. Which conclusion(s) logically follow from the statements?

A Only I follows B Only II follows C Both I and II follow D Neither I nor II follows

Why: Examining the logical structure: While all chairs are tables, and some tables are wooden, this does not establish a direct relationship between chairs and wooden objects. The wooden tables may or may not include chairs. We cannot conclude that all chairs are wooden (Conclusion I is invalid) because only some tables are wooden, not all. Similarly, we cannot conclude that some wooden objects are chairs (Conclusion II is invalid) because the wooden tables mentioned may not include any chairs. Both conclusions require information not provided by the premises, so neither logically follows.

Question 22

PYQ 1.0 marks

Statements: Some ants are parrots. All parrots are apples. Conclusions: I. All apples are parrots. II. Some ants are apples. Which conclusion(s) logically follow from the statements?

A Only I follows B Only II follows C Both I and II follow D Neither I nor II follows

Why: Analyzing the categorical syllogism: From 'Some ants are parrots' and 'All parrots are apples', we can deduce through the transitive property that some ants are apples (those ants that are parrots must be apples). This makes Conclusion II valid. However, Conclusion I states 'All apples are parrots', which is not supported by the premises. The second statement only tells us that all parrots are apples, not that all apples are parrots. This would be an invalid reversal of the categorical statement. Therefore, only Conclusion II logically follows.

Question 23

PYQ 1.0 marks

Statements: Some papers are pens. All pencils are pens. Conclusions: I. Some papers are pencils. II. All pens are papers. Which conclusion(s) logically follow from the statements?

A Only I follows B Only II follows C Both I and II follow D Neither I nor II follows

Why: Examining the logical relationships: The two statements tell us that some papers are pens and all pencils are pens. However, these statements do not establish a direct relationship between papers and pencils. Some papers being pens does not mean those papers are pencils, as pencils and papers are distinct categories that both happen to be pens. Conclusion I is invalid. Additionally, Conclusion II states 'All pens are papers', which contradicts the first statement and is not supported by the premises. The first statement only says some papers are pens, not that all pens are papers. Therefore, neither conclusion logically follows.

Question 24

PYQ 1.0 marks

Statements: Some horses are not trucks. All vehicles are trucks. Conclusions: I. Some horses are not vehicles. II. Some vehicles are horses. Which conclusion(s) logically follow from the statements?

A Only I follows B Only II follows C Both I and II follow D Neither I nor II follows

Why: Analyzing the syllogism: From 'Some horses are not trucks' and 'All vehicles are trucks', we can deduce that those horses which are not trucks cannot be vehicles (since all vehicles must be trucks). This makes Conclusion I valid: Some horses are not vehicles. However, Conclusion II states 'Some vehicles are horses', which is not supported by the premises. The statements establish that all vehicles are trucks and some horses are not trucks, but this does not mean any vehicles are horses. In fact, the logic suggests a separation between at least some horses and vehicles. Therefore, only Conclusion I logically follows.

Question 25

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Which of the following best describes a statement in logical reasoning?

A An expression that can be either true or false B A question asked to gather information C A command given to perform an action D An opinion that cannot be verified

Why: A statement in logical reasoning is a declarative sentence that is either true or false, but not both.

Question 26

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Consider the condition: "If it rains, then the ground will be wet." Which of the following is the contrapositive of this statement?

A If the ground is wet, then it rains B If the ground is not wet, then it does not rain C If it does not rain, then the ground is not wet D If the ground is wet, then it does not rain

Why: The contrapositive of "If P then Q" is "If not Q then not P", which in this case is "If the ground is not wet, then it does not rain."

Question 27

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Given the statement: "All birds can fly." Which of the following is a valid condition to test this statement?

A If an animal is a bird, then it can fly B If an animal can fly, then it is a bird C If an animal cannot fly, then it is not a bird D If an animal is not a bird, then it cannot fly

Why: The original statement implies that being a bird is sufficient to fly, so the condition "If an animal is a bird, then it can fly" directly tests the statement.

Question 28

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Consider the statement: "If a number is divisible by 4, then it is divisible by 2." Which of the following is NOT a valid conclusion?

A If a number is divisible by 4, it is divisible by 2 B If a number is not divisible by 2, it is not divisible by 4 C If a number is divisible by 2, it is divisible by 4 D If a number is not divisible by 4, it may or may not be divisible by 2

Why: The original statement does not imply that divisibility by 2 guarantees divisibility by 4, so conclusion C is invalid.

Question 29

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Statement: "All students who study regularly pass the exam." Which conclusion logically follows?

A Some students who do not study regularly pass the exam B No student who studies regularly fails the exam C All students who pass the exam study regularly D Some students who study regularly fail the exam

Why: If all students who study regularly pass, then none of them fail. Hence, conclusion B is valid.

Question 30

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Statement: "If the machine is switched on, it will start working." Which of the following conclusions is valid?

A If the machine is not working, it is not switched on B If the machine is working, it is switched on C If the machine is switched off, it will start working D The machine always works

Why: The contrapositive of the statement is "If the machine is not working, then it is not switched on," which is a valid conclusion.

Question 31

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Given: "All roses are flowers." Which of the following conclusions is logically valid?

A All flowers are roses B Some flowers are roses C No flower is a rose D Some roses are not flowers

Why: From "All roses are flowers," it follows that some flowers (at least the roses) exist, so some flowers are roses.

Question 32

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Statement: "If a person is a doctor, then they have a medical degree." Which conclusion is NOT valid?

A If a person does not have a medical degree, they are not a doctor B If a person has a medical degree, they are a doctor C If a person is a doctor, they have a medical degree D If a person is not a doctor, they may or may not have a medical degree

Why: Having a medical degree does not necessarily mean the person is a doctor; they could be a student or in another profession.

Question 33

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If the statement "All cats are mammals" is true, which of the following is a valid inference?

A All mammals are cats B Some mammals are cats C No mammals are cats D All cats are not mammals

Why: If all cats are mammals, then at least some mammals are cats (those cats).

Question 34

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Given the statement: "If it is a holiday, then the office is closed." Which of the following is a correct inference?

A If the office is not closed, then it is not a holiday B If the office is closed, then it is a holiday C If it is not a holiday, then the office is closed D If the office is open, then it is a holiday

Why: The contrapositive "If the office is not closed, then it is not a holiday" is a valid inference.

Question 35

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Statement: "If a person is eligible to vote, then they are above 18 years of age." Which of the following is a valid inference?

A If a person is below 18, they are not eligible to vote B If a person is above 18, they are eligible to vote C All people above 18 are eligible to vote D Some people below 18 are eligible to vote

Why: The contrapositive is valid: if a person is below 18, then they are not eligible to vote.

Question 36

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Consider the statement: "If the alarm rings, then there is a fire." Which of the following weakens this statement?

A The alarm rings only when there is a fire B Sometimes the alarm rings due to a system malfunction C There is always a fire when the alarm rings D The alarm never rings

Why: If the alarm rings sometimes due to malfunction, the statement that alarm ringing implies fire is weakened.

Question 37

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Statement: "If a student passes the exam, then they have studied." Which of the following is a valid conditional reasoning?

A If a student has studied, then they pass the exam B If a student has not studied, then they do not pass the exam C If a student passes the exam, then they have not studied D If a student does not pass the exam, then they have studied

Why: The contrapositive "If not studied, then not pass" is valid conditional reasoning.

Question 38

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Given: "If the traffic light is green, then vehicles can move." Which of the following is a valid medium-level conditional reasoning statement?

A If vehicles cannot move, then the traffic light is not green B If vehicles can move, then the traffic light is green C If the traffic light is not green, then vehicles can move D Vehicles move only if the traffic light is red

Why: The contrapositive "If vehicles cannot move, then the traffic light is not green" is valid.

Question 39

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Statement: "If a product is defective, then it will be returned." Which of the following is a hard-level conditional reasoning inference?

A If a product is not returned, then it is not defective B If a product is returned, then it is defective C All defective products are returned D Some defective products are not returned

Why: The contrapositive "If not returned, then not defective" is a valid inference, while the others may not necessarily hold.

Question 40

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Evaluate the assumption in the statement: "The company increased its advertising budget, so sales will increase." Which assumption is implicit?

A Increased advertising always leads to increased sales B Sales depend only on advertising C The product quality remains constant D Competitors have reduced their advertising

Why: The statement assumes that increasing advertising will cause sales to increase.

Question 41

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Statement: "If the government reduces taxes, then the economy will improve." Which assumption weakens this statement?

A Tax reduction always boosts the economy B Other factors may affect the economy more than taxes C Economy improves only with tax reduction D Taxes have no effect on the economy

Why: Assuming other factors may have more impact weakens the direct cause-effect relationship.

Question 42

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Which of the following is a hard-level question on evaluating assumptions in the statement: "The new policy will reduce unemployment."?

A The policy targets sectors with high unemployment B Unemployment depends on multiple factors C The policy is implemented effectively D The economy is stable

Why: Assuming unemployment depends on multiple factors challenges the direct effect of the policy.

Question 43

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Statement: "If the factory increases production, then profits will rise." Which assumption strengthens this statement?

A Demand for the product is high B Production costs will increase C Market is saturated D Competitors reduce prices

Why: High demand ensures that increased production leads to higher profits, strengthening the statement.

Question 44

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Statement: "Heavy rainfall causes flooding in the area." Which of the following best describes the cause-effect relationship here?

A Rainfall is the effect, flooding is the cause B Flooding causes heavy rainfall C Heavy rainfall is the cause, flooding is the effect D There is no relationship between rainfall and flooding

Why: Heavy rainfall is the cause that leads to the effect, flooding.

Question 45

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If a factory emits toxic gases, then nearby plants wither. Which of the following is a medium-level cause-effect analysis?

A Plants wither causes toxic gas emission B Toxic gas emission causes plants to wither C Plants wither and toxic gas emission are unrelated D Toxic gas emission is the effect of plant withering

Why: The emission of toxic gases is the cause; plant withering is the effect.

Question 46

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Statement: "Increased screen time leads to eye strain." Which of the following weakens this cause-effect relationship?

A Eye strain occurs only after prolonged screen time B Some people do not experience eye strain despite long screen time C Eye strain is always caused by screen time D Screen time is the only cause of eye strain

Why: If some people do not experience eye strain despite long screen time, the direct cause-effect relationship is weakened.

Question 47

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Statement: "If a statement is true, then its negation is false." Which of the following shows logical consistency?

A A statement and its negation can both be true B A statement and its negation cannot both be true C A statement and its negation are unrelated D Both a statement and its negation can be false

Why: Logical consistency requires that a statement and its negation cannot both be true simultaneously.

Question 48

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Which of the following pairs of statements is contradictory?

A "All birds can fly" and "Some birds cannot fly" B "Some cats are black" and "Some cats are white" C "All dogs are mammals" and "Some dogs are mammals" D "Some flowers are red" and "Some flowers are yellow"

Why: The statements "All birds can fly" and "Some birds cannot fly" cannot both be true, so they are contradictory.

Question 49

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Statement 1: "If it rains, the ground is wet." Statement 2: "The ground is not wet." Which of the following is logically consistent?

A It is raining B It is not raining C The ground is wet D It is raining and the ground is not wet

Why: If the ground is not wet, then it cannot be raining, which is logically consistent with statement 1.

Question 50

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Which of the following weakens the argument: "The new drug is effective because most patients recovered after taking it."?

A Patients recovered due to other treatments B The drug was administered properly C Most patients took the drug D The drug has no side effects

Why: If patients recovered due to other treatments, the argument that the drug caused recovery is weakened.

Question 51

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Statement: "Increasing exercise improves health." Which of the following strengthens this argument?

A Studies show regular exercise reduces disease risk B Exercise causes fatigue C Some people do not exercise regularly D Health depends on diet only

Why: Scientific studies supporting exercise benefits strengthen the argument.

Question 52

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Which of the following weakens the argument: "The company’s profits increased because of the new marketing strategy."?

A The market demand increased independently B The marketing strategy was innovative C Profits increased last year too D The company hired more staff

Why: If profits increased due to market demand, the role of marketing strategy is weakened.

Question 53

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Statement: "If the policy is implemented, unemployment will decrease." Which of the following strengthens this argument at a hard level?

A The policy targets sectors with high unemployment B Unemployment is affected by global trends C The policy is expensive to implement D Unemployment has decreased in the past

Why: Targeting sectors with high unemployment directly supports the argument that the policy will reduce unemployment.

Question 54

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Which of the following best describes a statement in logical reasoning?

A A sentence that expresses a fact or opinion and can be true or false B A question that requires an answer C An exclamation expressing emotion D A command given to someone

Why: A statement is a declarative sentence that can be assigned a truth value, either true or false, which is fundamental in logical reasoning.

Question 55

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Consider the statement: "If it rains, then the ground is wet." Which part of this statement is the condition?

A "It rains" B "The ground is wet" C "If it rains" D "Then the ground is wet"

Why: In an if-then statement, the 'if' part represents the condition or antecedent, which is "If it rains" in this case.

Question 56

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Given the statement: "All birds can fly." Which of the following is a valid conclusion?

A Penguins are birds and can fly. B Some birds cannot fly. C All flying creatures are birds. D Birds are animals that can fly.

Why: The statement implies that birds are animals capable of flying; however, it does not specify that all flying creatures are birds or that penguins can fly. Option D correctly restates the statement.

Question 57

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Statement: "If the alarm rings, then there is a fire." Which of the following conclusions is invalid?

A If there is no fire, the alarm does not ring. B If the alarm rings, there may be a fire. C If the alarm does not ring, there is no fire. D If there is a fire, the alarm rings.

Why: The original statement does not imply that every fire causes the alarm to ring (no converse). Hence, conclusion D is invalid.

Question 58

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If the statement "All cats are mammals" is true, which of the following is a logical implication?

A Some mammals are cats. B All mammals are cats. C No cats are mammals. D Some cats are not mammals.

Why: If all cats are mammals, then some mammals (at least those cats) are cats. The other options contradict the original statement.

Question 59

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Given: "If a student studies hard, then he will pass the exam." Which inference is logically correct?

A If a student passes the exam, he studied hard. B If a student does not study hard, he will fail the exam. C If a student does not pass the exam, he did not study hard. D If a student studies hard, he might pass the exam.

Why: The contrapositive of the statement is: If a student does not pass the exam, then he did not study hard, which is logically equivalent to the original statement.

Question 60

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Consider the statement: "If the traffic light is green, then vehicles can move." Which of the following is the converse of this statement?

A If vehicles can move, then the traffic light is green. B If the traffic light is not green, then vehicles cannot move. C If vehicles cannot move, then the traffic light is not green. D If the traffic light is green, then vehicles cannot move.

Why: The converse of an if-then statement switches the hypothesis and conclusion: If vehicles can move, then the traffic light is green.

Question 61

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Evaluate the assumption in the statement: "The factory stopped production because of a power outage." Which assumption is implicit?

A The factory can operate without power. B Power outage affects factory operations. C The factory stopped production for other reasons. D The factory has backup power supply.

Why: The statement assumes that a power outage impacts the factory's ability to produce, which is why production stopped.

Question 62

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Statement: "If the machine is faulty, then the output is defective." Which of the following is the negation of this statement?

A The machine is faulty and the output is not defective. B The machine is not faulty or the output is defective. C The machine is not faulty and the output is defective. D The machine is faulty or the output is defective.

Why: The negation of an if-then statement \( p \rightarrow q \) is \( p \wedge eg q \), meaning the machine is faulty but the output is not defective.

Question 63

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If "If it snows, then the roads are slippery" is true, which of the following is logically consistent with it?

A The roads are slippery only if it snows. B If the roads are slippery, then it snows. C If the roads are not slippery, then it does not snow. D It snows only when the roads are slippery.

Why: The contrapositive of the statement is: If the roads are not slippery, then it does not snow, which is logically equivalent and consistent.

Question 64

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Which of the following pairs of statements are contradictory?

A "All dogs are mammals." and "Some dogs are not mammals." B "If it rains, the ground is wet." and "If it rains, the ground is dry." C "Some birds can fly." and "Some birds cannot fly." D "All cars are vehicles." and "Some vehicles are cars."

Why: The statements "If it rains, the ground is wet" and "If it rains, the ground is dry" cannot both be true simultaneously, making them contradictory.

Question 65

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Cause and effect relationship: "Because the power went out, the computers shut down." Which of the following is the effect?

A Power went out B Computers shut down C Power was restored D Computers were turned on

Why: The effect is the event that happens as a result of the cause; here, the computers shutting down is the effect of the power outage.

Question 66

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Statement: "If the temperature rises above 30°C, then the ice cream melts." Which is the correct converse statement?

A If the ice cream melts, then the temperature rises above 30°C. B If the temperature does not rise above 30°C, then the ice cream does not melt. C If the ice cream does not melt, then the temperature does not rise above 30°C. D If the temperature rises above 30°C, then the ice cream does not melt.

Why: The converse of an if-then statement switches the hypothesis and conclusion: If the ice cream melts, then the temperature rises above 30°C.

Question 67

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Which of the following is a valid assumption in the statement: "The school canceled classes due to heavy rain."?

A Heavy rain affects school operations. B Classes were canceled for other reasons. C The school is always closed during rain. D Students prefer online classes.

Why: The statement assumes that heavy rain impacts the school's ability to conduct classes, leading to their cancellation.

Question 68

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If "If a person exercises regularly, then he is healthy" is true, which of the following is an invalid conclusion?

A A person who does not exercise regularly may not be healthy. B A healthy person exercises regularly. C A person who exercises regularly is healthy. D If a person is not healthy, then he does not exercise regularly.

Why: The original statement does not imply that all healthy people exercise regularly; hence conclusion B is invalid.

Question 69

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Which of the following statements is the negation of "All flowers are red"?

A No flowers are red. B Some flowers are not red. C All flowers are not red. D Some flowers are red.

Why: The negation of a universal affirmative statement "All flowers are red" is "Some flowers are not red."

Question 70

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Consider the statement: "If the engine fails, then the car stops." Which of the following is the contrapositive statement?

A If the car stops, then the engine fails. B If the car does not stop, then the engine does not fail. C If the engine does not fail, then the car stops. D If the car stops, then the engine does not fail.

Why: The contrapositive of \( p \rightarrow q \) is \( eg q \rightarrow eg p \), here: If the car does not stop, then the engine does not fail.

Question 71

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Which of the following best illustrates a cause and effect relationship?

A The sun rises in the east. B Because the heater was on, the room became warm. C Birds fly south in winter. D Water boils at 100°C.

Why: Option B clearly shows a cause (heater was on) leading to an effect (room became warm).

Question 72

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Statement: "If a person is a teacher, then he has a degree." Which of the following is a valid inference?

A All degree holders are teachers. B Some teachers do not have degrees. C If a person does not have a degree, then he is not a teacher. D If a person has a degree, then he is a teacher.

Why: The contrapositive of the statement is: If a person does not have a degree, then he is not a teacher, which is a valid inference.

Question 73

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Which of the following pairs of statements are logically consistent?

A "All cats are animals." and "Some animals are cats." B "No birds can fly." and "Some birds can fly." C "If it rains, then the ground is wet." and "If it rains, the ground is dry." D "All cars are vehicles." and "No vehicles are cars."

Why: The statements "All cats are animals" and "Some animals are cats" can both be true simultaneously, so they are logically consistent.

Question 74

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If "If the light is on, then the room is bright" is true, which of the following is the correct inverse statement?

A If the light is off, then the room is not bright. B If the room is not bright, then the light is off. C If the room is bright, then the light is on. D If the light is on, then the room is not bright.

Why: The inverse of \( p \rightarrow q \) is \( eg p \rightarrow eg q \), which here is: If the light is off, then the room is not bright.

Question 75

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Statement: "If the software is updated, then the system runs faster." Which of the following is a valid conclusion?

A If the system runs faster, the software is updated. B If the software is not updated, the system does not run faster. C If the system does not run faster, the software is not updated. D If the software is updated, the system may run slower.

Why: The contrapositive is: If the system does not run faster, then the software is not updated, which is logically equivalent and valid.

Question 76

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Which of the following statements best shows logical inconsistency?

A "Some fruits are sweet." and "All fruits are sweet." B "All dogs bark." and "Some dogs do not bark." C "If it rains, then the ground is wet." and "If it rains, then the ground is wet." D "All cars have wheels." and "Some cars have wheels."

Why: The statements "All dogs bark" and "Some dogs do not bark" contradict each other, showing logical inconsistency.

Question 77

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Cause and effect: "Due to the heavy snowfall, the airport was closed." Which of the following is the cause?

A Airport was closed B Heavy snowfall C Flights were delayed D Passengers were stranded

Why: The cause is the event that leads to another event; here, heavy snowfall caused the airport closure.

Question 78

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Which of the following is the converse of the statement: "If a person is a doctor, then he has a medical degree."?

A If a person has a medical degree, then he is a doctor. B If a person is not a doctor, then he does not have a medical degree. C If a person does not have a medical degree, then he is not a doctor. D If a person is a doctor, then he does not have a medical degree.

Why: The converse switches the hypothesis and conclusion: If a person has a medical degree, then he is a doctor.

Question 79

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In a certain logical system, the statement "If P then Q" is true. Additionally, it is known that "If Q then R" is false, and "If R then P" is true. Given these conditions, which of the following must be true?

A P is false B Q is false C R is true D P and R are both true

Why: Step 1: "If P then Q" is true, so whenever P is true, Q must be true. Step 2: "If Q then R" is false, meaning there exists a case where Q is true but R is false. Step 3: "If R then P" is true, so whenever R is true, P must be true. Step 4: From Step 2, since "If Q then R" is false, Q can be true and R false. Step 5: But if R is false, from Step 3, no conclusion about P directly, but from Step 1, if P were true, Q would be true. Step 6: Since Q can be true with R false, and R false means P may not be true (otherwise R would be true by Step 3). Step 7: Therefore, P must be false to allow Q true and R false. Step 8: Hence, Q is false is incorrect; P is false is correct. But option B says Q is false, which contradicts Step 2. Re-examining: Since "If Q then R" is false, Q true and R false possible. If P true, Q true (Step 1), so Q true. Since Q true and R false, P true leads to contradiction with Step 3. Therefore, P must be false. Option A is correct. Reconsidering options, correct answer is A.

Question 80

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Consider the statements: (1) If a number is divisible by 7, then it is divisible by 21. (2) If a number is divisible by 21, then it is divisible by 3. (3) If a number is divisible by 3, then it is divisible by 7. Which of the following is logically consistent?

A Only statement (2) is true B Statements (1) and (2) are true, (3) is false C All three statements are true D Statements (2) and (3) are true, (1) is false

Why: Step 1: Analyze statement (1): "If divisible by 7, then divisible by 21". - This is false because 7 divides 7 but 21 does not divide 7. Step 2: Statement (2): "If divisible by 21, then divisible by 3". - True because 21 = 3*7. Step 3: Statement (3): "If divisible by 3, then divisible by 7". - False because 3 divides 3 but 7 does not divide 3. Step 4: So (1) is false, (2) is true, (3) is false. Step 5: Check options: Option D says (2) and (3) true, (1) false - but (3) is false. Option B says (1) and (2) true, (3) false - (1) is false. Option A says only (2) true - matches our analysis. Option C all true - no. Step 6: Correct answer is A.

Question 81

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Given the statements: (i) If the system is secure, then the data is encrypted. (ii) If the data is encrypted, then the key is complex. (iii) The key is not complex. Which of the following conclusions is logically valid?

A The system is not secure B The data is not encrypted C Both the system is not secure and the data is not encrypted D No conclusion can be drawn

Why: Step 1: From (ii), "If data encrypted then key complex". Step 2: Given key is not complex, so by contrapositive of (ii), data is not encrypted. Step 3: From (i), "If system secure then data encrypted". Step 4: Since data not encrypted, contrapositive of (i) implies system not secure. Step 5: Therefore, both system is not secure and data is not encrypted. Step 6: Option C matches this conclusion.

Question 82

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In a logic puzzle, the following statements are given: 1. If the door is locked, then the alarm is on. 2. The alarm is not on if and only if the window is open. 3. The window is closed. Which of the following is true?

A The door is locked B The door is not locked C The alarm is on and the door is locked D The alarm is off and the door is locked

Why: Step 1: From (3), window is closed. Step 2: From (2), alarm is not on iff window is open. Step 3: Since window is closed, alarm is on. Step 4: From (1), if door locked then alarm on. Step 5: Alarm is on, but door could be locked or not. Step 6: However, if door were locked, alarm must be on (true). Step 7: But alarm on does not imply door locked. Step 8: So door may or may not be locked. Step 9: But since alarm is on and window is closed, door is not necessarily locked. Step 10: Option B says door is not locked, which is the only definite conclusion given window closed and alarm on. Step 11: Actually, no direct conclusion about door locked can be drawn. Step 12: Reconsider options: Option B says door not locked (definite), which is not necessarily true. Option A says door locked (not necessarily true). Option C says alarm on and door locked (alarm on true, door locked uncertain). Option D says alarm off and door locked (alarm off false). Step 13: Only alarm on is certain. Step 14: So none of the options except C partially true. Step 15: But door locked not certain. Step 16: So best answer is C (alarm on and door locked) - alarm on true, door locked possible. Step 17: But question asks which is true, so option C is best. Step 18: Correct answer is C.

Question 83

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A statement S is defined as: "If and only if P is true, then Q is false." Given that P and Q are boolean variables, which of the following is logically equivalent to S?

A P ↔ ¬Q B ¬P ↔ Q C P → ¬Q D ¬P → Q

Why: Step 1: The statement "If and only if P is true, then Q is false" means P is true exactly when Q is false. Step 2: This is the biconditional P ↔ ¬Q. Step 3: Option A matches this. Step 4: Option B is the negation of P biconditional with Q, which is not equivalent. Step 5: Options C and D are one-way implications, not biconditionals. Step 6: Hence, correct answer is A.

Question 84

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In a system, the following conditions hold: (i) If the sensor detects motion, then the light turns on. (ii) The light is off only if the power is out. (iii) The power is not out. Which of the following can be logically concluded?

A The sensor does not detect motion B The light is on C The sensor detects motion and the light is on D No conclusion about the sensor detecting motion

Why: Step 1: From (iii), power is not out. Step 2: From (ii), light is off only if power is out. Step 3: Since power not out, light cannot be off. Step 4: Therefore, light is on. Step 5: From (i), if sensor detects motion, light turns on. Step 6: But light on does not imply sensor detects motion (light could be on for other reasons). Step 7: So no conclusion about sensor detecting motion. Step 8: Hence, correct answer is D.

Question 85

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Consider the statements: 1. If the machine is faulty, then the alarm sounds. 2. The alarm does not sound if and only if the machine is not faulty. 3. The alarm sounds. Which of the following is true?

A The machine is faulty B The machine is not faulty C Cannot determine if the machine is faulty D The alarm sounds regardless of the machine's condition

Why: Step 1: Statement (2) is a biconditional: alarm does not sound iff machine not faulty. Step 2: So alarm sounds iff machine faulty. Step 3: Given alarm sounds (3), so machine is faulty. Step 4: Hence, option A is correct.

Question 86

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A statement is given: "If the temperature is below 15.7°C, then the heater is on. If the heater is on, then the electricity consumption is above 120.3 units. If the electricity consumption is not above 120.3 units, then the temperature is not below 15.7°C." Which of the following is logically consistent with these statements?

A Temperature below 15.7°C and electricity consumption below 120.3 units B Temperature above or equal to 15.7°C and electricity consumption above 120.3 units C Temperature below 15.7°C and electricity consumption above 120.3 units D Temperature above or equal to 15.7°C and electricity consumption below or equal to 120.3 units

Why: Step 1: From first statement: temp < 15.7 → heater on. Step 2: From second: heater on → consumption > 120.3. Step 3: From third: consumption ≤ 120.3 → temp ≥ 15.7 (contrapositive of first two). Step 4: Combining, temp < 15.7 implies consumption > 120.3. Step 5: So temp < 15.7 and consumption ≤ 120.3 is impossible. Step 6: Option A is impossible. Step 7: Option B says temp ≥ 15.7 and consumption > 120.3, which is possible but not guaranteed. Step 8: Option C says temp < 15.7 and consumption > 120.3, which is consistent. Step 9: Option D says temp ≥ 15.7 and consumption ≤ 120.3, also consistent. Step 10: But question asks for logically consistent with all statements. Step 11: Both C and D are consistent, but only C matches the direct implications. Step 12: Correct answer is C.

Question 87

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In a logical framework, the following is true: - Statement A implies Statement B. - Statement B implies Statement C. - Statement C is false. Which of the following can be concluded?

A Statement A is false B Statement B is false C Both Statement A and B are false D No conclusion about Statement A

Why: Step 1: Given A → B and B → C. Step 2: C is false. Step 3: From B → C and C false, contrapositive: C false → B false. Step 4: So B is false. Step 5: From A → B and B false, contrapositive: B false → A false. Step 6: So A is false. Step 7: Therefore, both A and B are false. Step 8: Option C is correct.

Question 88

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Match the following statements with their correct logical equivalences: Statements: 1. "If P then Q" 2. "P if and only if Q" 3. "P unless Q" 4. "Neither P nor Q" Options: A. ¬P ∨ Q B. (P → Q) ∧ (Q → P) C. ¬P ∧ ¬Q D. P ∨ ¬Q Which of the following is the correct matching?

A 1-A, 2-B, 3-D, 4-C B 1-B, 2-A, 3-C, 4-D C 1-D, 2-C, 3-A, 4-B D 1-C, 2-D, 3-B, 4-A

Why: Step 1: "If P then Q" is logically equivalent to ¬P ∨ Q (Option A). Step 2: "P if and only if Q" is biconditional (P → Q) ∧ (Q → P) (Option B). Step 3: "P unless Q" means if not Q then P, which is P ∨ ¬Q (Option D). Step 4: "Neither P nor Q" means ¬P ∧ ¬Q (Option C). Step 5: So matching is 1-A, 2-B, 3-D, 4-C. Step 6: Option A matches this.

Question 89

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Consider the statement: "If the code passes all tests, then it is bug-free. However, the code is not bug-free. Additionally, if the code is bug-free, then the documentation is complete." Which of the following is true?

A The code does not pass all tests and documentation is incomplete B The code passes all tests but documentation is incomplete C The code does not pass all tests but documentation is complete D No conclusion about documentation

Why: Step 1: "If code passes all tests then bug-free". Step 2: Code is not bug-free. Step 3: Contrapositive of Step 1: Not bug-free → code does not pass all tests. Step 4: So code does not pass all tests. Step 5: "If bug-free then documentation complete". Step 6: Code is not bug-free, so no guarantee about documentation. Step 7: But since code not bug-free, documentation completeness is not guaranteed. Step 8: So documentation may be incomplete. Step 9: Option A says code does not pass all tests and documentation incomplete. Step 10: Documentation incomplete is plausible but not certain. Step 11: Option D says no conclusion about documentation, which is more precise. Step 12: But question asks which is true, so safest is D. Step 13: However, since bug-free implies documentation complete, not bug-free implies documentation may be incomplete. Step 14: So option A is best. Step 15: Correct answer is A.

Question 90

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In a scenario, the following statements hold: - If the system is online, then the server is active. - If the server is active, then the backup is running. - The backup is not running. Which of the following is a valid conclusion?

A The system is offline B The server is inactive C Both the system is offline and the server is inactive D No conclusion about the system's status

Why: Step 1: Given: system online → server active. Step 2: server active → backup running. Step 3: backup not running. Step 4: Contrapositive of step 2: backup not running → server inactive. Step 5: Contrapositive of step 1: server inactive → system offline. Step 6: From backup not running, server inactive. Step 7: From server inactive, system offline. Step 8: Hence, both system offline and server inactive. Step 9: Option C is correct.

Question 91

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Given the statements: (i) If the project is delayed, then the budget will be exceeded. (ii) The budget is not exceeded. (iii) If the budget is exceeded, then the client will be unhappy. Which of the following is true?

A The project is not delayed and the client is happy B The project is delayed and the client is unhappy C The project is not delayed but the client is unhappy D No conclusion about the client's happiness

Why: Step 1: From (i), delayed → budget exceeded. Step 2: From (ii), budget not exceeded. Step 3: Contrapositive of (i): budget not exceeded → project not delayed. Step 4: So project not delayed. Step 5: From (iii), budget exceeded → client unhappy. Step 6: Budget not exceeded, so client not unhappy (client happy). Step 7: Option A matches both conclusions.

Question 92

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Assertion (A): "If a statement is true, then its negation is false." Reason (R): "A statement and its negation cannot both be true simultaneously." Choose the correct option:

A Both A and R are true and R is the correct explanation of A B Both A and R are true but R is not the correct explanation of A C A is true but R is false D A is false but R is true

Why: Step 1: Assertion states a fundamental logical principle: if a statement is true, its negation must be false. Step 2: Reason states that a statement and its negation cannot both be true simultaneously. Step 3: Reason correctly explains why assertion holds. Step 4: Both are true and R explains A. Step 5: Hence, option A is correct.

Question 93

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Match the following logical connectives with their truth-functional definitions: Statements: 1. NAND 2. NOR 3. XOR 4. XNOR Options: A. True only when both inputs are false B. True when inputs differ C. False only when both inputs are true D. True when inputs are equal Which of the following is the correct matching?

A 1-C, 2-A, 3-B, 4-D B 1-A, 2-C, 3-D, 4-B C 1-B, 2-D, 3-A, 4-C D 1-D, 2-B, 3-C, 4-A

Why: Step 1: NAND is false only when both inputs are true (Option C). Step 2: NOR is true only when both inputs are false (Option A). Step 3: XOR is true when inputs differ (Option B). Step 4: XNOR is true when inputs are equal (Option D). Step 5: So matching is 1-C, 2-A, 3-B, 4-D. Step 6: Option A matches this.

Question 94

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If the statement "If P then Q" is false, which of the following must be true?

A P is true and Q is false B P is false and Q is true C Both P and Q are false D Both P and Q are true

Why: Step 1: "If P then Q" is false only when P is true and Q is false. Step 2: Otherwise, the implication is true. Step 3: Hence, option A is correct.

Question 95

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Given the statements: (i) If the system is compromised, then the firewall is disabled. (ii) The firewall is enabled. (iii) If the firewall is enabled, then the system is secure. Which of the following is correct?

A The system is compromised B The system is secure C The firewall status is irrelevant to system security D Cannot determine system security

Why: Step 1: From (ii), firewall enabled. Step 2: From (iii), firewall enabled → system secure. Step 3: So system is secure. Step 4: From (i), system compromised → firewall disabled. Step 5: Firewall enabled means system not compromised. Step 6: Hence, system is secure. Step 7: Option B is correct.

Question 96

Question bank

Which of the following best defines a statement in logical reasoning?

A A sentence that expresses a fact or opinion and can be either true or false B A question that requires an answer C An exclamation expressing emotion D A command or request

Why: A statement is a declarative sentence that is either true or false, which is fundamental in logical reasoning.

Question 97

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Identify which of the following is NOT a statement:

A "The Earth revolves around the Sun." B "Is it raining outside?" C "Water boils at 100 degrees Celsius." D "All humans are mortal."

Why: A question is not a statement because it does not declare something that can be true or false.

Question 98

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Given the statement: "All birds can fly," which of the following conclusions logically follows?

A Penguins can fly. B Some birds cannot fly. C All animals can fly. D Birds are animals.

Why: The statement implies birds are a category of animals, so 'Birds are animals' is a valid conclusion.

Question 99

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Which of the following is a type of conclusion in logical reasoning?

A Definite conclusion B Indefinite conclusion C Possible conclusion D All of the above

Why: Conclusions can be definite, indefinite, or possible depending on the strength of the logical connection to the statement.

Question 100

Question bank

Statement: "All roses are flowers. Some flowers fade quickly." Which conclusion is valid?

A All roses fade quickly. B Some roses may fade quickly. C No rose fades quickly. D All flowers are roses.

Why: Since some flowers fade quickly and roses are flowers, it is possible some roses fade quickly, but not certain.

Question 101

Question bank

Which of the following conclusions is an example of a possible conclusion?

A All cats are mammals. B Some cats are black. C No cat is a reptile. D All cats are black.

Why: The conclusion 'Some cats are black' is possible based on general knowledge but not definite from a given statement.

Question 102

Question bank

Statement: "No reptiles are warm-blooded. All snakes are reptiles." Which conclusion is valid?

A Some snakes are warm-blooded. B No snake is warm-blooded. C All warm-blooded animals are snakes. D Some reptiles are warm-blooded.

Why: Since no reptiles are warm-blooded and all snakes are reptiles, no snake can be warm-blooded.

Question 103

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Statement: "Some students are athletes. All athletes are disciplined." Which conclusion is definitely valid?

A Some students are disciplined. B All students are disciplined. C No student is disciplined. D All athletes are students.

Why: Since some students are athletes and all athletes are disciplined, some students are disciplined.

Question 104

Question bank

Which factor is most important in evaluating the validity of a conclusion drawn from a statement?

A The number of words in the statement B The logical connection between the statement and conclusion C The popularity of the statement D The length of the conclusion

Why: Validity depends on the logical connection between the statement and the conclusion, not on superficial factors.

Question 105

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Statement: "All cars are vehicles. Some vehicles are electric." Which conclusion is valid?

A All cars are electric. B Some cars may be electric. C No car is electric. D All electric things are cars.

Why: Since some vehicles are electric and all cars are vehicles, some cars may be electric but it is not definite.

Question 106

Question bank

Statement: "No birds are mammals. All sparrows are birds." Which conclusion is valid?

A Some sparrows are mammals. B No sparrow is a mammal. C All mammals are sparrows. D Some mammals are birds.

Why: Since no birds are mammals and sparrows are birds, no sparrow can be a mammal.

Question 107

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Statement: "All engineers are logical. Some logical people are creative." Which conclusion is valid?

A All engineers are creative. B Some engineers may be creative. C No engineer is creative. D All creative people are engineers.

Why: Since some logical people are creative and all engineers are logical, some engineers may be creative but not necessarily all.

Question 108

Question bank

Which of the following is a valid logical deduction technique?

A Assuming the conclusion is true without evidence B Using syllogisms to infer conclusions from premises C Ignoring contradictory evidence D Drawing conclusions based on emotions

Why: Syllogistic reasoning is a valid logical deduction technique to infer conclusions from given premises.

Question 109

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Statement: "All mammals are warm-blooded. All whales are mammals." Which conclusion follows by logical deduction?

A All whales are warm-blooded. B Some whales are not warm-blooded. C No whale is warm-blooded. D All warm-blooded animals are whales.

Why: Since all mammals are warm-blooded and whales are mammals, all whales are warm-blooded.

Question 110

Question bank

Which of the following is an example of a logical deduction technique?

A Inductive reasoning B Syllogistic reasoning C Guesswork D Emotional appeal

Why: Syllogistic reasoning is a formal method of logical deduction using premises to reach conclusions.

Question 111

Question bank

Statement: "Some fruits are sweet. All apples are fruits." Which conclusion can be logically deduced?

A All apples are sweet. B Some apples may be sweet. C No apple is sweet. D All sweet things are apples.

Why: Since some fruits are sweet and apples are fruits, some apples may be sweet but not necessarily all.

Question 112

Question bank

Which of the following is a common logical fallacy when drawing conclusions?

A Affirming the consequent B Modus ponens C Modus tollens D Disjunctive syllogism

Why: Affirming the consequent is a logical fallacy where one assumes the cause from the effect incorrectly.

Question 113

Question bank

Statement: "If it rains, the ground is wet. The ground is wet." Which fallacy is committed if one concludes "It rained"?

A Affirming the consequent B Denying the antecedent C Circular reasoning D Straw man

Why: Affirming the consequent fallacy occurs when one assumes the cause because the effect is observed, which may not be true.

Question 114

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Which of the following is an example of a logical fallacy in conclusions?

A Assuming correlation implies causation B Using valid syllogisms C Drawing conclusions from true premises D Applying deductive reasoning

Why: Assuming correlation implies causation is a common logical fallacy leading to invalid conclusions.

Question 115

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Statement: "All dogs bark. Some animals bark." Which conclusion is an example of a logical fallacy if stated as "All animals that bark are dogs"?

A Hasty generalization B Affirming the consequent C Begging the question D False cause

Why: Assuming 'All animals that bark are dogs' affirms the consequent and is a logical fallacy.

Question 116

Question bank

In syllogistic reasoning, which of the following is a valid syllogism?

A All men are mortal. Socrates is a man. Therefore, Socrates is mortal. B All birds can fly. Penguins are birds. Therefore, penguins can fly. C Some cats are black. All cats are animals. Therefore, some animals are black. D All flowers are plants. Some plants are trees. Therefore, some flowers are trees.

Why: The first syllogism is valid as the conclusion logically follows from the premises.

Question 117

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Statement: "No reptiles are warm-blooded. All snakes are reptiles." Which conclusion is valid using syllogistic reasoning?

A Some snakes are warm-blooded. B No snake is warm-blooded. C All warm-blooded animals are snakes. D Some reptiles are warm-blooded.

Why: Using syllogistic reasoning, since no reptiles are warm-blooded and snakes are reptiles, no snake is warm-blooded.

Question 118

Question bank

Which of the following syllogisms is invalid?

A All flowers are plants. Some plants are trees. Therefore, some flowers are trees. B All men are mortal. Socrates is a man. Therefore, Socrates is mortal. C No reptiles are warm-blooded. All snakes are reptiles. Therefore, no snake is warm-blooded. D All cars are vehicles. Some vehicles are electric. Therefore, some cars may be electric.

Why: The conclusion that some flowers are trees does not logically follow from the premises.

Question 119

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Statement: "If the power supply fails, the machine stops. The machine has stopped." Which conclusion is valid regarding cause and effect?

A The power supply has definitely failed. B The machine stopped due to power supply failure or other reasons. C The machine is functioning properly. D The power supply is working.

Why: The machine stopping could be caused by power failure or other reasons; the cause is not definite.

Question 120

Question bank

Which of the following best illustrates a cause and effect relationship?

A It rained heavily, so the streets are flooded. B The streets are flooded, so it must have rained heavily. C People like ice cream, so it is summer. D The sun is shining, so it is daytime.

Why: Heavy rain causing flooded streets is a direct cause and effect relationship.

Question 121

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Statement: "The factory stopped production because of a power outage." Which of the following is a valid inference?

A Power outage caused the factory to stop production. B The factory stopped production for unknown reasons. C The factory never stops production. D The factory stopped production due to worker strike.

Why: The statement explicitly states the power outage caused the stoppage, so this is a valid inference.

Question 122

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Statement: "All successful entrepreneurs take risks." Which assumption is implicit in this statement?

A Taking risks is necessary for success in entrepreneurship. B Some entrepreneurs do not take risks. C Risk-taking always leads to failure. D Entrepreneurs avoid risks.

Why: The statement assumes that risk-taking is necessary for entrepreneurial success.

Question 123

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Statement: "The new policy will reduce pollution." Which inference can be drawn?

A The policy is designed to address pollution. B Pollution will increase due to the policy. C The policy is unrelated to pollution. D Pollution is not a problem.

Why: The statement implies the policy aims to reduce pollution, so it is designed to address it.

Question 124

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Statement: "If the alarm rings, there is a fire." The alarm is ringing. Which assumption is valid?

A There is definitely a fire. B The alarm can ring without fire. C The fire alarm is broken. D There is no fire.

Why: The statement assumes that the alarm ringing indicates a fire, so the assumption is that there is a fire.

Question 125

Question bank

Statement: "All students passed the exam." Which inference is incorrect?

A Some students scored very high marks. B No student failed the exam. C All students scored the same marks. D Every student passed.

Why: The statement does not imply all students scored the same marks, so this inference is incorrect.

Question 126

Question bank

Which of the following best describes a statement in logical reasoning?

A A sentence that expresses a fact or opinion and can be true or false B A question that requires an answer C An exclamation expressing emotion D A command or request

Why: A statement is a declarative sentence that is either true or false, which is fundamental to logical reasoning.

Question 127

Question bank

Identify which of the following is NOT a statement:

A "The sky is blue." B "Is it raining today?" C "Water boils at 100°C." D "2 + 2 = 4."

Why: A question does not assert a fact and cannot be true or false, so it is not a statement.

Question 128

Question bank

Which of the following statements is a factual statement?

A "All birds can fly." B "The Earth revolves around the Sun." C "Chocolate is the best ice cream flavor." D "Tomorrow will be sunny."

Why: The statement about Earth revolving around the Sun is a scientifically proven fact.

Question 129

Question bank

Given the statement: "If it rains, the ground will be wet." Which of the following conclusions is definitely true?

A The ground is wet only if it rains. B If the ground is wet, it has rained. C If it rains, then the ground is wet. D The ground is never wet.

Why: The statement is a conditional: if it rains, then the ground will be wet. This conclusion restates the original statement and is definitely true.

Question 130

Question bank

Statement: "All roses are flowers. Some flowers fade quickly." Which conclusion is definitely true?

A All roses fade quickly. B Some roses may fade quickly. C No roses fade quickly. D All flowers are roses.

Why: Since some flowers fade quickly and all roses are flowers, it is possible that some roses fade quickly, but it is not definite.

Question 131

Question bank

Statement: "The library is closed on Sundays." Which of the following conclusions is NOT possible?

A The library is open on weekdays. B The library is closed on Sundays. C The library is open on Sundays. D The library is closed on public holidays.

Why: The statement explicitly says the library is closed on Sundays, so it cannot be open on Sundays.

Question 132

Question bank

Statement: "Some students are athletes." Which conclusion is definitely true?

A All students are athletes. B Some athletes are students. C No students are athletes. D All athletes are students.

Why: If some students are athletes, then it is definitely true that some athletes are students.

Question 133

Question bank

Statement: "If the alarm rings, then there is a fire." Which conclusion is definitely true?

A If there is a fire, the alarm will ring. B If the alarm rings, there is a fire. C If there is no fire, the alarm will ring. D The alarm rings only when there is no fire.

Why: The statement is a conditional 'if p then q'; the conclusion restates this and is definitely true.

Question 134

Question bank

Statement: "No cats are dogs. Some pets are cats." Which conclusion is possible?

A Some pets are not dogs. B All pets are dogs. C No pets are cats. D All cats are dogs.

Why: Since some pets are cats and cats are not dogs, it is possible that some pets are not dogs.

Question 135

Question bank

Statement: "All engineers are problem solvers. Some problem solvers are artists." Which conclusion is NOT possible?

A Some engineers are artists. B All problem solvers are engineers. C Some artists are problem solvers. D All engineers are problem solvers.

Why: The statement does not say all problem solvers are engineers, so this conclusion is not possible.

Question 136

Question bank

Statement: "If it is a weekend, the park is crowded." Which conclusion is logically valid?

A If the park is crowded, it is a weekend. B If it is not a weekend, the park is not crowded. C If it is a weekend, the park is crowded. D The park is crowded every day.

Why: The statement is a conditional 'if p then q'; only conclusion C restates it correctly and is valid.

Question 137

Question bank

Statement: "Some fruits are sweet. All apples are fruits." Which conclusion is valid?

A All apples are sweet. B Some apples may be sweet. C No apples are sweet. D All fruits are apples.

Why: Since some fruits are sweet and all apples are fruits, it is possible that some apples are sweet.

Question 138

Question bank

Statement: "If the machine is on, it produces noise." Which conclusion is invalid?

A If there is noise, the machine is on. B If the machine is off, there is no noise. C If the machine is on, it produces noise. D The machine produces noise only when it is on.

Why: The original statement does not imply that noise only occurs if the machine is on, so conclusion A is invalid.

Question 139

Question bank

Statement: "All birds have wings. Penguins are birds." Which conclusion is logically valid?

A Penguins have wings. B All birds can fly. C Penguins can fly. D Some birds do not have wings.

Why: Since all birds have wings and penguins are birds, penguins have wings is valid, though they cannot fly.

Question 140

Question bank

Statement: "If a student studies hard, then he will pass the exam." Which conclusion is definitely true?

A If the student passes, he studied hard. B If the student does not study hard, he will fail. C If the student studies hard, he will pass. D If the student fails, he did not study hard.

Why: The statement is a conditional 'if p then q'; only conclusion C restates this correctly and is definitely true.

Question 141

Question bank

Statement: "Some cars are electric. All electric vehicles are eco-friendly." Which conclusion is valid?

A Some cars are eco-friendly. B All cars are eco-friendly. C No cars are eco-friendly. D All electric vehicles are cars.

Why: Since some cars are electric and all electric vehicles are eco-friendly, some cars are eco-friendly is valid.

Question 142

Question bank

Statement: "All mammals are warm-blooded. Whales are mammals." Which conclusion is logically valid?

A Whales are warm-blooded. B All warm-blooded animals are mammals. C Whales are fish. D Some mammals are not warm-blooded.

Why: Since all mammals are warm-blooded and whales are mammals, whales are warm-blooded is logically valid.

Question 143

Question bank

Statement: "All teachers are educated. Some educated people are musicians." Which conclusion can be inferred?

A Some teachers are musicians. B All musicians are educated. C Some educated people are teachers. D All teachers are musicians.

Why: Since all teachers are educated, some educated people being musicians does not imply teachers are musicians, but some educated people are teachers.

Question 144

Question bank

Statement: "No reptiles have feathers. Some animals with feathers can fly." Which conclusion is valid?

A Some reptiles can fly. B No reptiles have feathers. C All animals with feathers are reptiles. D Some animals with feathers cannot fly.

Why: The statement explicitly says no reptiles have feathers, so conclusion B is valid.

Question 145

Question bank

Statement: "If it is a holiday, the office is closed. Today is not a holiday." Which conclusion is possible?

A The office is closed today. B The office is open today. C Today is a holiday. D The office is always closed.

Why: Since today is not a holiday, the office may be open; the statement does not guarantee closure on non-holidays.

Question 146

Question bank

Statement: "All fruits have seeds. Tomatoes have seeds." Which conclusion is valid?

A Tomatoes are fruits. B All tomatoes are fruits. C Some fruits are tomatoes. D Tomatoes are not fruits.

Why: Since all fruits have seeds and tomatoes have seeds, it is valid to conclude tomatoes are fruits based on the statement.

Question 147

Question bank

Statement: "If the power goes out, the alarm will stop working." The alarm is not working. Which conclusion is valid?

A The power has gone out. B The alarm is broken. C The power may have gone out. D The alarm is working.

Why: If the alarm is not working, the power may have gone out, but it could also be due to other reasons; hence, conclusion C is valid.

Question 148

Question bank

Statement: "All politicians are honest. Some honest people are lawyers." Which conclusion contains a logical fallacy?

A Some politicians are lawyers. B All honest people are politicians. C Some lawyers are honest. D All politicians are honest.

Why: The statement does not imply all honest people are politicians; this is a logical fallacy (affirming the consequent).

Question 149

Question bank

Statement: "If it rains, the streets get wet. The streets are wet." Which conclusion is a logical fallacy?

A It has rained. B The streets are wet. C If it rains, the streets get wet. D The streets are wet because it rained.

Why: Assuming it has rained because the streets are wet is affirming the consequent, a logical fallacy.

Question 150

Question bank

Statement: "All dogs bark. Max is a dog. Max barks." Which conclusion is a logical fallacy?

A Max is a dog because he barks. B Max barks because he is a dog. C All dogs bark. D Max is a dog.

Why: Concluding Max is a dog just because he barks is affirming the consequent, a logical fallacy.

Question 151

Question bank

Statement: "If a student passes the exam, then he has studied. John has studied." Which conclusion is a logical fallacy?

A John will pass the exam. B John has studied. C If a student passes, then he has studied. D John may pass the exam.

Why: The statement does not guarantee that studying always leads to passing; concluding John will pass is affirming the antecedent but may not be valid.

Question 152

Question bank

Statement: "All cats are animals. Some animals are pets. Some cats are pets." Which conclusion is logically valid using syllogistic reasoning?

A All cats are pets. B Some cats are pets. C No cats are pets. D All animals are cats.

Why: Since some animals are pets and all cats are animals, it is valid that some cats are pets.

Question 153

Question bank

Statement: "All engineers are logical. Some logical people are creative." Which conclusion follows from syllogistic reasoning?

A Some engineers are creative. B All logical people are engineers. C Some creative people are engineers. D All engineers are creative.

Why: Since some logical people are creative and all engineers are logical, some engineers may be creative.

Question 154

Question bank

Statement: "If a person exercises regularly, then he is healthy. Some healthy people are athletes." Which conclusion is valid using syllogistic reasoning?

A All athletes exercise regularly. B Some athletes are healthy. C All healthy people are athletes. D Some athletes do not exercise.

Why: Since some healthy people are athletes, it is valid that some athletes are healthy.

Question 155

Question bank

Statement: "If it rains, the ground gets wet. It is raining." Which conclusion is valid using conditional reasoning?

A The ground is wet. B The ground is dry. C It is not raining. D The ground may be wet or dry.

Why: Given the condition and the fact it is raining, the ground getting wet is a valid conclusion.

Question 156

Question bank

Statement: "If the traffic light is red, vehicles stop. Vehicles are stopped." Which conclusion is a logical fallacy in causal reasoning?

A The traffic light is red. B Vehicles stopped because the light is red. C Vehicles are stopped. D The traffic light may be red or green.

Why: Assuming the traffic light is red just because vehicles stopped is affirming the consequent, a logical fallacy.

Question 157

Question bank

Statement: "All students who study hard pass the exam. John passed the exam." Which conclusion is an assumption rather than a fact?

A John studied hard. B John passed the exam. C All students who study hard pass. D Some students do not pass.

Why: Passing the exam does not necessarily mean John studied hard; assuming so is an assumption, not a fact.

Question 158

Question bank

Statement: "The factory emits smoke. The air quality is poor." Which conclusion is an assumption?

A The factory causes poor air quality. B The air quality is poor. C The factory emits smoke. D Smoke emission affects air quality.

Why: Assuming the factory causes poor air quality is an assumption; correlation does not imply causation.

Question 159

Question bank

Statement: "All birds have feathers. Penguins have feathers." Which conclusion is an assumption?

A Penguins are birds. B Penguins have feathers. C All birds have feathers. D Some birds cannot fly.

Why: Assuming penguins are birds just because they have feathers is an assumption; other animals may have feathers too.

Question 160

Question bank

Statement: "All the members of a certain club are either engineers or doctors. Some engineers are not members of the club. Some members of the club are doctors who do not attend the monthly meetings." Conclusions: I. All doctors attend the monthly meetings. II. Some members of the club are engineers who attend the monthly meetings. III. Some engineers are not members of the club. IV. No doctor who is not a member of the club attends the monthly meetings. Which of the following is correct?

A Only III is definitely true B Only II and III are definitely true C Only I and IV are definitely true D Only II, III, and IV are definitely true

Why: Step 1: From the statement, all club members are engineers or doctors. Step 2: Some engineers are not members of the club (explicitly stated). Step 3: Some doctors who are members do not attend meetings. Step 4: Conclusion I says all doctors attend meetings, which contradicts step 3, so I is false. Step 5: Conclusion II says some club engineers attend meetings. Since some doctors don't attend, and all members are engineers or doctors, some engineers must attend meetings to fulfill the club's meeting attendance. Step 6: Conclusion III is explicitly stated. Step 7: Conclusion IV says no doctor outside the club attends meetings. The statement doesn't mention doctors outside the club, so this cannot be concluded definitively. Therefore, only II and III are definitely true.

Question 161

Question bank

Statement: "No student who studies mathematics is lazy. Some students who study physics are lazy. All students who study chemistry study mathematics." Conclusions: I. Some students who study chemistry are not lazy. II. No student who studies physics studies mathematics. III. Some lazy students study physics. IV. All students who study chemistry are not lazy. Which of the following is correct?

A Only I and III are true B Only II and IV are true C Only III and IV are true D Only I, III, and IV are true

Why: Step 1: No math students are lazy → all math students are not lazy. Step 2: Some physics students are lazy → lazy physics students exist. Step 3: All chemistry students study math → chemistry students are a subset of math students. Step 4: Since chemistry students study math, and math students are not lazy, chemistry students are not lazy. Step 5: Conclusion I: Some chemistry students are not lazy — true (all are not lazy). Step 6: Conclusion II: No physics student studies math — not necessarily true; statement doesn't say physics students don't study math. Step 7: Conclusion III: Some lazy students study physics — true (given). Step 8: Conclusion IV: All chemistry students are not lazy — true (from step 4). Therefore, I, III, and IV are true.

Question 162

Question bank

Statement: "All vehicles with registration numbers ending in an odd digit are inspected every 7 days. Some vehicles with registration numbers ending in 3 are exempt from inspection. No vehicle exempt from inspection is allowed to operate on highways." Conclusions: I. Some vehicles with registration numbers ending in 3 are inspected every 7 days. II. No vehicle with registration numbers ending in an odd digit operates on highways. III. Some vehicles with registration numbers ending in 3 are not allowed on highways. IV. All vehicles inspected every 7 days operate on highways. Which of the following is correct?

A Only I and III are true B Only II and IV are true C Only I, III, and IV are true D Only III is true

Why: Step 1: All vehicles with odd-ending registration numbers are inspected every 7 days. Step 2: Some vehicles ending in 3 are exempt from inspection (subset of odd-ending vehicles). Step 3: No exempt vehicle operates on highways. Step 4: Conclusion I: Some vehicles ending in 3 are inspected (since only some are exempt, others are inspected) — true. Step 5: Conclusion II: No odd-ending vehicle operates on highways — false, since only exempt vehicles don't operate on highways; others could. Step 6: Conclusion III: Some vehicles ending in 3 are not allowed on highways (the exempt ones) — true. Step 7: Conclusion IV: All inspected vehicles operate on highways — not necessarily true; statement doesn't say inspected vehicles must operate on highways. Therefore, only I and III are true.

Question 163

Question bank

Statement: "Every employee who works in department A or department B has completed training X. Some employees who completed training X do not work in department A. No employee who works in department B has completed training Y." Conclusions: I. Some employees who completed training X work in department B. II. Some employees who completed training Y do not work in department B. III. All employees who completed training Y work outside departments A and B. IV. Some employees who completed training X work in department A. Which of the following is correct?

A Only I and IV are true B Only II and III are true C Only I, II, and IV are true D Only III is true

Why: Step 1: All employees in A or B completed training X. Step 2: Some employees who completed training X do not work in A (could be in B or other departments). Step 3: No employee in B completed training Y. Step 4: Conclusion I: Some employees who completed training X work in B — true (since B employees completed X). Step 5: Conclusion II: Some employees who completed training Y do not work in B — true (no B employee completed Y, so all Y-trained employees are outside B). Step 6: Conclusion III: All employees who completed Y work outside A and B — not necessarily true; statement only excludes B, not A. Step 7: Conclusion IV: Some employees who completed X work in A — true (since all A employees completed X). Therefore, I, II, and IV are true.

Question 164

Question bank

Statement: "All the devices manufactured by Company P are tested for quality. Some devices tested for quality are not approved for sale. No device not approved for sale is sold in international markets." Conclusions: I. Some devices manufactured by Company P are not approved for sale. II. All devices sold in international markets are approved for sale. III. Some devices not tested for quality are sold in international markets. IV. No device manufactured by Company P is sold in international markets without approval. Which of the following is correct?

A Only I, II, and IV are true B Only II and III are true C Only I and IV are true D Only II is true

Why: Step 1: All Company P devices are tested. Step 2: Some tested devices are not approved. Step 3: No device not approved is sold internationally. Step 4: Conclusion I: Some Company P devices are not approved — true (since some tested devices are not approved, and all Company P devices are tested). Step 5: Conclusion II: All devices sold internationally are approved — true (no unapproved device sold internationally). Step 6: Conclusion III: Some devices not tested are sold internationally — false (Company P devices all tested; others not specified, but statement implies tested devices only). Step 7: Conclusion IV: No Company P device sold internationally without approval — true (all Company P devices tested, some not approved, and unapproved not sold internationally). Therefore, I, II, and IV are true.

Question 165

Question bank

Statement: "If a person is a member of Club X, then they have passed Exam A. Some persons who passed Exam A have not joined Club X. No person who has not passed Exam A is a member of Club X." Conclusions: I. All members of Club X have passed Exam A. II. Some persons who passed Exam A are not members of Club X. III. No person who has not passed Exam A is a member of Club X. IV. Some persons who are not members of Club X have passed Exam A. Which of the following is correct?

A Only I and II are true B Only I, II, and III are true C Only II, III, and IV are true D All I, II, III, and IV are true

Why: Step 1: If member of Club X → passed Exam A. Step 2: Some who passed Exam A have not joined Club X. Step 3: No person who has not passed Exam A is a member of Club X. Step 4: Conclusion I: All members passed Exam A — true (from Step 1). Step 5: Conclusion II: Some who passed Exam A are not members — true (Step 2). Step 6: Conclusion III: No one who hasn't passed Exam A is a member — true (Step 3). Step 7: Conclusion IV: Some not members have passed Exam A — true (Step 2). Therefore, all conclusions are true.

Question 166

Question bank

Statement: "Every product that is eco-friendly is either biodegradable or recyclable. Some products that are biodegradable are not eco-friendly. No recyclable product is harmful to the environment." Conclusions: I. Some eco-friendly products are recyclable. II. All biodegradable products are eco-friendly. III. Some products that are not eco-friendly are biodegradable. IV. No harmful product is recyclable. Which of the following is correct?

A Only I, III, and IV are true B Only II and IV are true C Only I and IV are true D Only III and IV are true

Why: Step 1: All eco-friendly products are biodegradable or recyclable. Step 2: Some biodegradable products are not eco-friendly. Step 3: No recyclable product is harmful. Step 4: Conclusion I: Some eco-friendly products are recyclable — possible and likely true (since eco-friendly products are either biodegradable or recyclable). Step 5: Conclusion II: All biodegradable products are eco-friendly — false (Step 2 says some biodegradable are not eco-friendly). Step 6: Conclusion III: Some non-eco-friendly products are biodegradable — true (Step 2). Step 7: Conclusion IV: No harmful product is recyclable — true (Step 3). Therefore, I, III, and IV are true.

Question 167

Question bank

Statement: "All authors who write fiction have won at least one literary award. Some authors who have won literary awards do not write fiction. No author who writes fiction has never won an award." Conclusions: I. Some authors who have won literary awards do not write fiction. II. All authors who write fiction have won awards. III. No author who writes fiction has never won an award. IV. Some authors who write fiction have not won awards. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: All fiction authors have won awards. Step 2: Some award winners do not write fiction. Step 3: No fiction author has never won an award → all fiction authors have won awards. Step 4: Conclusion I: Some award winners do not write fiction — true (Step 2). Step 5: Conclusion II: All fiction authors have won awards — true (Step 1). Step 6: Conclusion III: No fiction author has never won an award — true (Step 3). Step 7: Conclusion IV: Some fiction authors have not won awards — false (contradicts Step 1 and 3). Therefore, only I, II, and III are true.

Question 168

Question bank

Statement: "If a machine is automated, then it is efficient. Some machines are efficient but not automated. No machine that is not efficient is automated." Conclusions: I. All automated machines are efficient. II. Some efficient machines are not automated. III. No inefficient machine is automated. IV. Some automated machines are inefficient. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: If automated → efficient. Step 2: Some efficient machines are not automated. Step 3: No inefficient machine is automated. Step 4: Conclusion I: All automated machines are efficient — true (Step 1). Step 5: Conclusion II: Some efficient machines are not automated — true (Step 2). Step 6: Conclusion III: No inefficient machine is automated — true (Step 3). Step 7: Conclusion IV: Some automated machines are inefficient — false (contradicts Step 1 and 3). Therefore, only I, II, and III are true.

Question 169

Question bank

Statement: "All participants who scored above 85 passed the exam. Some participants who passed the exam scored below 60. No participant who scored below 60 failed the exam." Conclusions: I. Some participants who scored below 60 passed the exam. II. All participants who scored above 85 passed the exam. III. No participant who scored below 60 failed the exam. IV. Some participants who passed the exam scored above 85. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I, III, and IV are true D Only I, II, III, and IV are true

Why: Step 1: All scoring above 85 passed. Step 2: Some who passed scored below 60. Step 3: No one scoring below 60 failed. Step 4: Conclusion I: Some below 60 passed — true (Step 2). Step 5: Conclusion II: All above 85 passed — true (Step 1). Step 6: Conclusion III: No below 60 failed — true (Step 3). Step 7: Conclusion IV: Some who passed scored above 85 — true (Step 1). Therefore, all conclusions are true.

Question 170

Question bank

Statement: "If a book is a bestseller, then it is widely available. Some books that are widely available are not bestsellers. No book that is not widely available is a bestseller." Conclusions: I. All bestsellers are widely available. II. Some widely available books are not bestsellers. III. No book that is not widely available is a bestseller. IV. Some bestsellers are not widely available. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: Bestseller → widely available. Step 2: Some widely available books are not bestsellers. Step 3: No book not widely available is a bestseller. Step 4: Conclusion I: All bestsellers are widely available — true (Step 1). Step 5: Conclusion II: Some widely available books are not bestsellers — true (Step 2). Step 6: Conclusion III: No book not widely available is a bestseller — true (Step 3). Step 7: Conclusion IV: Some bestsellers are not widely available — false (contradicts Step 1 and 3). Therefore, only I, II, and III are true.

Question 171

Question bank

Statement: "All vehicles that use fuel type X are subject to emission tests. Some vehicles subject to emission tests do not use fuel type X. No vehicle that does not use fuel type X is exempt from emission tests." Conclusions: I. Some vehicles subject to emission tests do not use fuel type X. II. All vehicles that use fuel type X are subject to emission tests. III. No vehicle that does not use fuel type X is exempt from emission tests. IV. Some vehicles that use fuel type X are exempt from emission tests. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: All vehicles using fuel X are tested. Step 2: Some tested vehicles do not use fuel X. Step 3: No vehicle not using fuel X is exempt from tests. Step 4: Conclusion I: Some tested vehicles do not use fuel X — true (Step 2). Step 5: Conclusion II: All vehicles using fuel X are tested — true (Step 1). Step 6: Conclusion III: No vehicle not using fuel X is exempt — true (Step 3). Step 7: Conclusion IV: Some vehicles using fuel X are exempt — false (contradicts Step 1). Therefore, only I, II, and III are true.

Question 172

Question bank

Statement: "If a student is enrolled in course A or course B, then they have access to the online portal. Some students with access to the online portal are not enrolled in course A. No student without access to the online portal is enrolled in course B." Conclusions: I. Some students enrolled in course B have access to the online portal. II. Some students with access to the online portal are not enrolled in course B. III. No student without access to the online portal is enrolled in course B. IV. All students enrolled in course A have access to the online portal. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I, III, and IV are true D Only I, II, III, and IV are true

Why: Step 1: Enrollment in A or B → access to portal. Step 2: Some with access are not enrolled in A. Step 3: No one without access is enrolled in B. Step 4: Conclusion I: Some enrolled in B have access — true (Step 1). Step 5: Conclusion II: Some with access are not enrolled in B — true (Step 2). Step 6: Conclusion III: No one without access is enrolled in B — true (Step 3). Step 7: Conclusion IV: All enrolled in A have access — true (Step 1). Therefore, all conclusions are true.

Question 173

Question bank

Statement: "All employees who work night shifts receive a bonus. Some employees who receive bonuses do not work night shifts. No employee who does not receive a bonus works night shifts." Conclusions: I. Some employees who receive bonuses do not work night shifts. II. All employees who work night shifts receive bonuses. III. No employee who does not receive a bonus works night shifts. IV. Some employees who work night shifts do not receive bonuses. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: All night shift employees receive bonuses. Step 2: Some bonus recipients do not work night shifts. Step 3: No non-bonus recipient works night shifts. Step 4: Conclusion I: Some bonus recipients do not work night shifts — true (Step 2). Step 5: Conclusion II: All night shift employees receive bonuses — true (Step 1). Step 6: Conclusion III: No non-bonus recipient works night shifts — true (Step 3). Step 7: Conclusion IV: Some night shift employees do not receive bonuses — false (contradicts Step 1). Therefore, only I, II, and III are true.

Question 174

Question bank

Statement: "All smartphones with feature X support 5G connectivity. Some smartphones that support 5G do not have feature X. No smartphone without feature X supports 5G connectivity." Conclusions: I. All smartphones with feature X support 5G connectivity. II. Some smartphones that support 5G do not have feature X. III. No smartphone without feature X supports 5G connectivity. IV. Some smartphones with feature X do not support 5G connectivity. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: All smartphones with feature X support 5G. Step 2: Some 5G-supporting smartphones do not have feature X. Step 3: No smartphone without feature X supports 5G. Step 4: Conclusion I: All with feature X support 5G — true (Step 1). Step 5: Conclusion II: Some 5G supporters lack feature X — true (Step 2). Step 6: Conclusion III: No smartphone without feature X supports 5G — true (Step 3). Step 7: Conclusion IV: Some with feature X do not support 5G — false (contradicts Step 1). Therefore, only I, II, and III are true.

Question 175

Question bank

Statement: "If a city has a metro system, then it has a population above 500,000. Some cities with populations above 500,000 do not have metro systems. No city without a metro system has a population above 500,000." Conclusions: I. All cities with metro systems have populations above 500,000. II. Some cities with populations above 500,000 do not have metro systems. III. No city without a metro system has a population above 500,000. IV. Some cities with metro systems have populations below 500,000. Which of the following is correct?

A Only I, II, and III are true B Only II and IV are true C Only I and III are true D Only I, II, III, and IV are true

Why: Step 1: Metro system → population > 500,000. Step 2: Some cities with population > 500,000 lack metro systems. Step 3: No city without metro has population > 500,000. Step 4: Conclusion I: All metro cities have population > 500,000 — true (Step 1). Step 5: Conclusion II: Some cities with population > 500,000 lack metro — true (Step 2). Step 6: Conclusion III: No city without metro has population > 500,000 — true (Step 3). Step 7: Conclusion IV: Some metro cities have population < 500,000 — false (contradicts Step 1). Therefore, only I, II, and III are true.

Question 176

Question bank

Which of the following best defines a syllogism in logical reasoning?

A A form of argument with two premises and a conclusion B A statement that is always true C A type of fallacy in reasoning D A method to solve equations

Why: A syllogism is a logical argument that applies deductive reasoning to arrive at a conclusion based on two premises.

Question 177

Question bank

In syllogistic logic, what is the term for the statement that follows from the premises?

A Premise B Conclusion C Major term D Minor term

Why: The conclusion is the statement that logically follows from the given premises in a syllogism.

Question 178

Question bank

Identify the middle term in the following syllogism: "All cats are animals. All animals are living beings. Therefore, all cats are living beings."

A Cats B Animals C Living beings D None of the above

Why: The middle term appears in both premises but not in the conclusion. Here, 'animals' is the middle term.

Question 179

Question bank

Which type of syllogism is represented by the statement: "If it rains, then the ground is wet. It is raining. Therefore, the ground is wet."?

A Categorical syllogism B Conditional syllogism C Disjunctive syllogism D Hypothetical syllogism

Why: This is a conditional syllogism where the first premise is a conditional statement, and the conclusion follows from the affirmation of the antecedent.

Question 180

Question bank

Which of the following is an example of a disjunctive syllogism?

A Either the light is on or the fan is running. The light is not on. Therefore, the fan is running. B If it is sunny, then we will go to the park. It is sunny. Therefore, we will go to the park. C All birds are animals. All animals are living beings. Therefore, all birds are living beings. D No cats are dogs. All dogs are animals. Therefore, no cats are animals.

Why: Disjunctive syllogism involves a disjunction (either/or statement) and the negation of one disjunct leading to the affirmation of the other.

Question 181

Question bank

Which of the following is NOT a valid type of categorical proposition?

A A: Universal Affirmative B E: Universal Negative C I: Particular Affirmative D U: Universal Conditional

Why: The standard forms of categorical propositions are A, E, I, and O. 'U' is not a recognized form.

Question 182

Question bank

Identify the form of the proposition: "Some students are not athletes."

A A (Universal Affirmative) B E (Universal Negative) C I (Particular Affirmative) D O (Particular Negative)

Why: The proposition states a particular negative, which corresponds to the O form.

Question 183

Question bank

Which of the following correctly represents the proposition "No dogs are cats" in standard form?

A All dogs are cats. B No dogs are cats. C Some dogs are cats. D Some dogs are not cats.

Why: The proposition is a universal negative, represented by E form: No S are P.

Question 184

Question bank

Which of the following is a valid rule for a categorical syllogism?

A The middle term must be distributed at least once. B The conclusion can distribute a term not distributed in the premises. C Both premises can be particular. D The conclusion can be stronger than the premises.

Why: One key rule is that the middle term must be distributed at least once in the premises for the syllogism to be valid.

Question 185

Question bank

In a valid syllogism, which of the following is true regarding the distribution of terms?

A If a term is distributed in the conclusion, it must be distributed in the premises. B Terms can be distributed in the conclusion but not in the premises. C The middle term must never be distributed. D The conclusion can distribute any term regardless of premises.

Why: A valid syllogism requires that any term distributed in the conclusion must be distributed in the premises.

Question 186

Question bank

Which of the following syllogisms violates the rule that the middle term must be distributed at least once?

A All cats are animals. All dogs are animals. Therefore, all cats are dogs. B All cats are animals. Some animals are dogs. Therefore, some cats are dogs. C No cats are dogs. All dogs are animals. Therefore, no cats are animals. D Some cats are animals. Some animals are dogs. Therefore, some cats are dogs.

Why: In option D, the middle term (animals) is not distributed in either premise, violating the rule.

Question 187

Question bank

Which of the following syllogisms is invalid due to drawing a conclusion from two negative premises?

A No cats are dogs. No dogs are birds. Therefore, no cats are birds. B All cats are animals. Some animals are dogs. Therefore, some cats are dogs. C All birds are animals. All animals are living beings. Therefore, all birds are living beings. D Some cats are animals. Some animals are dogs. Therefore, some cats are dogs.

Why: A syllogism with two negative premises is invalid because no conclusion can be drawn.

Question 188

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Refer to the diagram below. Which region represents "All A are B" in the Venn diagram with circles A and B?

A The entire circle A inside circle B B The entire circle B inside circle A C The overlapping part of A and B shaded D The part of A outside B shaded

Why: In "All A are B", circle A is entirely within circle B, meaning all elements of A are also in B.

Question 189

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Refer to the Venn diagram below showing three sets A, B, and C. Which conclusion is valid if the shaded area represents "No A are B"?

A Some A are B B No A are B C All A are B D Some B are A

Why: The shaded area indicates no overlap between A and B, so "No A are B" is valid.

Question 190

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Refer to the Venn diagram below with three circles A, B, and C. If the shaded area represents "Some A are B", which of the following is true?

A All A are B B No A are B C At least one element is common to A and B D All B are A

Why: The shaded overlapping region indicates that some elements belong to both A and B.

Question 191

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Refer to the Venn diagram below. Which of the following conclusions is valid if the shaded area represents "All B are C"?

A Some B are not C B All B are C C No B are C D Some C are not B

Why: The shading shows that circle B is entirely within circle C, representing "All B are C".

Question 192

Question bank

Which of the following arguments is valid based on the rules of syllogism?

A All men are mortal. Socrates is a man. Therefore, Socrates is mortal. B All men are mortal. Socrates is mortal. Therefore, Socrates is a man. C Some men are mortal. Socrates is a man. Therefore, Socrates is mortal. D No men are mortal. Socrates is a man. Therefore, Socrates is not mortal.

Why: The first argument is a classic valid syllogism with a universal affirmative major premise and a particular minor premise.

Question 193

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Given the premises: "All A are B" and "Some C are A", which of the following conclusions is valid?

A Some C are B B All C are B C No C are B D All A are C

Why: Since all A are B and some C are A, it follows that some C are B.

Question 194

Question bank

Which of the following syllogisms is invalid?

A All flowers are plants. Some plants are trees. Therefore, some flowers are trees. B All dogs are animals. All animals are mortal. Therefore, all dogs are mortal. C No cats are dogs. All dogs are animals. Therefore, no cats are animals. D Some birds are animals. All animals are living beings. Therefore, some birds are living beings.

Why: The conclusion in option A does not logically follow from the premises; it commits the fallacy of the undistributed middle.

Question 195

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Refer to the diagram below. Based on the shaded regions, which conclusion is valid from the premises "All A are B" and "No B are C"?

A No A are C B Some A are C C All C are A D Some B are C

Why: If all A are B and no B are C, then no A can be C, as A is a subset of B.

Question 196

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From the statements: "Some students are athletes." and "All athletes are disciplined.", which conclusion follows?

A Some students are disciplined. B All students are disciplined. C No students are disciplined. D Some athletes are students.

Why: Since some students are athletes and all athletes are disciplined, some students are disciplined.

Question 197

Question bank

Which of the following is a common logical fallacy in syllogisms?

A Affirming the consequent B Modus ponens C Disjunctive syllogism D Hypothetical syllogism

Why: Affirming the consequent is a logical fallacy where one assumes the converse of a conditional statement is true.

Question 198

Question bank

Which fallacy is committed in the argument: "If it rains, the ground is wet. The ground is wet. Therefore, it rained."?

A Affirming the consequent B Denying the antecedent C Modus tollens D Disjunctive syllogism

Why: This argument assumes that because the consequent is true, the antecedent must be true, which is a fallacy.

Question 199

Question bank

Which of the following is an example of the fallacy of the undistributed middle?

A All cats are animals. All dogs are animals. Therefore, all cats are dogs. B If it rains, the ground is wet. It is raining. Therefore, the ground is wet. C No cats are dogs. All dogs are animals. Therefore, no cats are animals. D Some birds are animals. All animals are living beings. Therefore, some birds are living beings.

Why: The middle term 'animals' is not distributed in either premise, making the syllogism invalid.

Question 200

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In a chain syllogism, if "All A are B", "All B are C", and "All C are D", which conclusion is valid?

A All A are D B All D are A C Some A are D D No A are D

Why: By transitivity, if all A are B, all B are C, and all C are D, then all A are D.

Question 201

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Consider the following chain of syllogisms: "All M are N", "All N are P", "All P are Q". Which of the following conclusions is correct?

A All M are Q B Some M are Q C No M are Q D Some Q are M

Why: By chaining the premises, all M are Q follows logically.

Question 202

Question bank

Which of the following symbolic representations correctly translates the statement "All S are P"?

A \( \forall x (S(x) \rightarrow P(x)) \) B \( \exists x (S(x) \wedge P(x)) \) C \( \forall x (P(x) \rightarrow S(x)) \) D \( \exists x (S(x) \rightarrow P(x)) \)

Why: The universal affirmative "All S are P" is symbolized as \( \forall x (S(x) \rightarrow P(x)) \).

Question 203

Question bank

Translate the proposition "Some A are not B" into symbolic form.

A \( \exists x (A(x) \wedge eg B(x)) \) B \( \forall x (A(x) \rightarrow B(x)) \) C \( \exists x (A(x) \wedge B(x)) \) D \( \forall x (A(x) \wedge eg B(x)) \)

Why: The particular negative proposition "Some A are not B" is represented as \( \exists x (A(x) \wedge eg B(x)) \).

Question 204

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Which symbolic representation corresponds to the disjunctive syllogism: "Either P or Q. Not P. Therefore, Q."?

A \( (P \lor Q) \wedge eg P \rightarrow Q \) B \( (P \wedge Q) \wedge eg P \rightarrow Q \) C \( (P \lor Q) \wedge P \rightarrow Q \) D \( (P \wedge Q) \wedge Q \rightarrow P \)

Why: Disjunctive syllogism is symbolized as \( (P \lor Q) \wedge eg P \rightarrow Q \).

Question 205

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Refer to the diagram below. Which of the following conclusions is valid based on the shaded areas representing "Some A are B" and "No B are C"?

A Some A are not C B All A are C C No A are B D All B are C

Why: Since some A are B and no B are C, it follows that some A are not C.

Question 206

Question bank

In a complex syllogism, if "All A are B", "No B are C", and "Some C are D", which of the following conclusions is valid?

A No A are C B Some D are B C Some A are D D No D are A

Why: Since no B are C and all A are B, it follows that no A are C.

Question 207

Question bank

Which of the following is a valid symbolic translation of the argument: "If P then Q. If Q then R. Therefore, if P then R."?

A \( (P \rightarrow Q) \wedge (Q \rightarrow R) \rightarrow (P \rightarrow R) \) B \( (P \wedge Q) \rightarrow R \) C \( (P \rightarrow R) \wedge (Q \rightarrow P) \) D \( (R \rightarrow Q) \wedge (Q \rightarrow P) \)

Why: This is the hypothetical syllogism rule, symbolized as \( (P \rightarrow Q) \wedge (Q \rightarrow R) \rightarrow (P \rightarrow R) \).

Question 208

Question bank

Which of the following best defines a categorical syllogism?

A An argument with two premises and a conclusion involving categories B An argument based on if-then statements C An argument involving either-or statements D An argument that uses numerical data to reach conclusions

Why: A categorical syllogism consists of two premises and a conclusion, each statement relating categories or classes of things.

Question 209

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In syllogistic terminology, what is the 'middle term'?

A The term that appears in both premises but not in the conclusion B The term that appears only in the conclusion C The term that appears in the conclusion and one premise D The term that is the subject of the conclusion

Why: The middle term connects the two premises but does not appear in the conclusion, serving as the link between the other terms.

Question 210

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Which of the following statements is NOT true about a valid syllogism?

A The middle term must be distributed at least once B If both premises are true, the conclusion must be true C The conclusion can have a term not present in the premises D The conclusion follows logically from the premises

Why: A valid syllogism cannot have a conclusion containing a term not present in the premises; this would be a fallacy.

Question 211

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Identify the type of syllogism in the statement: "If it rains, then the ground is wet. It is raining. Therefore, the ground is wet."

A Categorical syllogism B Conditional syllogism C Disjunctive syllogism D Hypothetical syllogism

Why: This is a conditional syllogism because it involves an if-then statement and a direct affirmation of the antecedent.

Question 212

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Which of the following is an example of a disjunctive syllogism?

A Either the light is on or the fan is on. The light is on. Therefore, the fan is off. B If the alarm rings, then there is a fire. The alarm rings. Therefore, there is a fire. C All birds are animals. All animals have cells. Therefore, all birds have cells. D Either the train arrives on time or it is delayed. The train is not delayed. Therefore, it arrives on time.

Why: A disjunctive syllogism involves an either-or premise and the negation of one option leading to the affirmation of the other.

Question 213

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Consider the syllogism: "All cats are mammals. Some mammals are carnivores. Therefore, some cats are carnivores." What type of syllogism is this?

A Categorical syllogism B Conditional syllogism C Disjunctive syllogism D Invalid syllogism

Why: This syllogism involves categorical statements about classes and subsets, making it a categorical syllogism.

Question 214

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If the premises are: "Either the project is delayed or the budget is exceeded." and "The project is not delayed.", what conclusion can be drawn?

A The budget is exceeded. B The project is delayed. C The budget is not exceeded. D No conclusion can be drawn.

Why: From the disjunctive premise and negation of one option, the other must be true.

Question 215

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Identify the correct Venn diagram representation for the syllogism: "All A are B. All B are C. Therefore, all A are C." Refer to the diagram below.

A Diagram shows circle A completely inside B, and B completely inside C B Diagram shows circle A overlapping B, and B overlapping C C Diagram shows circle A outside B, and B inside C D Diagram shows circles A, B, and C all separate

Why: The correct Venn diagram for this syllogism shows nested circles representing the subset relations.

Question 216

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Refer to the diagram below. Which conclusion is valid based on the Venn diagram showing "Some A are B" and "No B are C"?

A Some A are not C B All A are C C No A are B D All B are C

Why: Since no B are C and some A are B, those A that are B cannot be C, so some A are not C.

Question 217

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Refer to the diagram below. Given the premises "All M are P" and "Some S are M", which conclusion is supported?

A Some S are P B All S are P C No S are P D All M are S

Why: Since all M are P and some S are M, those S that are M must be P, so some S are P.

Question 218

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Refer to the diagram below. Which of the following conclusions is invalid based on the Venn diagram representing "No A are B" and "Some B are C"?

A No A are C B Some C are not A C Some B are C D No A are B

Why: The diagram shows no overlap between A and B but some overlap between B and C; no direct conclusion about A and C can be made.

Question 219

Question bank

Which of the following is a valid rule for syllogistic arguments?

A The middle term must be undistributed in both premises B If a term is distributed in the conclusion, it must be distributed in the premise C Both premises can be negative for a valid conclusion D The conclusion can be broader than the premises

Why: A term distributed in the conclusion must be distributed in the premises to avoid invalid conclusions.

Question 220

Question bank

Given the premises: "No A are B" and "All C are B", which conclusion is valid?

A No C are A B Some C are not A C All A are C D Some A are C

Why: Since no A are B and all C are B, none of the C can be A, so no C are A.

Question 221

Question bank

Which of the following violates the rules of a valid syllogism?

A Both premises are affirmative and conclusion is affirmative B One premise is negative and conclusion is affirmative C Both premises are negative D Middle term is distributed in at least one premise

Why: A syllogism with two negative premises is invalid because no conclusion can be drawn.

Question 222

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If the premises are "All A are B" and "Some C are not B", which conclusion is logically valid?

A Some C are not A B All C are A C No conclusion can be drawn D All A are C

Why: The premises do not provide enough information to conclude anything definite about C and A.

Question 223

Question bank

From the statements "All dogs are animals" and "Some animals are pets", which conclusion is valid?

A Some dogs are pets B All pets are dogs C Some animals are dogs D No conclusion can be drawn about dogs being pets

Why: The premises do not provide enough information to conclude about dogs being pets.

Question 224

Question bank

Given the statements: "All fruits are edible" and "Some fruits are sour", which conclusion is logically valid?

A Some edible things are sour B All sour things are fruits C No edible things are sour D All fruits are sour

Why: Since all fruits are edible and some fruits are sour, some edible things are sour.

Question 225

Question bank

If the premises are "No A are B" and "Some C are A", what conclusion follows?

A Some C are not B B All C are B C No C are B D No conclusion can be drawn

Why: The premises do not provide sufficient information to conclude about C and B.

Question 226

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Which of the following is an example of the fallacy of the undistributed middle?

A All cats are animals. All dogs are animals. Therefore, all cats are dogs. B If it rains, the ground is wet. It is raining. Therefore, the ground is wet. C Either the light is on or the fan is on. The light is off. Therefore, the fan is on. D All birds have wings. Some animals have wings. Therefore, some animals are birds.

Why: The middle term 'animals' is not distributed in either premise, leading to an invalid conclusion.

Question 227

Question bank

Identify the fallacy in the syllogism: "All A are B. Some C are not A. Therefore, some C are not B."

A Illicit major B Illicit minor C Fallacy of exclusive premises D Fallacy of drawing a negative conclusion from affirmative premises

Why: The major term B is distributed in the conclusion but not in the premise, an illicit major fallacy.

Question 228

Question bank

Which fallacy is committed in the argument: "If it is a dog, then it is an animal. It is an animal. Therefore, it is a dog."?

A Affirming the consequent B Denying the antecedent C Undistributed middle D False dichotomy

Why: Affirming the consequent is a fallacy where the consequent is affirmed to conclude the antecedent.

Question 229

Question bank

Which of the following is an example of the fallacy of exclusive premises?

A No A are B. No C are B. Therefore, no C are A. B All A are B. Some B are C. Therefore, some A are C. C If A then B. Not B. Therefore, not A. D Either A or B. Not A. Therefore, B.

Why: Both premises are negative, which is not allowed in a valid syllogism, causing the fallacy of exclusive premises.

Question 230

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A company has employees who are either managers or engineers. Some engineers are part-time. Which conclusion is valid?

A Some managers are part-time B All part-time employees are engineers C Some employees are part-time D No managers are engineers

Why: Since some engineers are part-time and engineers are employees, some employees are part-time.

Question 231

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If "All students who study hard pass exams" and "Some students who pass exams participate in sports", which conclusion is valid?

A Some students who study hard participate in sports B All students who participate in sports study hard C No students who study hard participate in sports D Some students who do not study hard pass exams

Why: Since some students who pass exams participate in sports and all who study hard pass exams, some who study hard participate in sports.

Question 232

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A survey shows: "Either a person is employed or is a student." "Some students are part-time workers." Which conclusion is valid?

A Some employed persons are students B All part-time workers are students C No employed persons are students D Some students are not employed

Why: Since some students are part-time workers (employed), some students are not employed is not necessarily true; however, since the premise is an either-or, some students may not be employed.

Question 233

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Refer to the diagram below. Given the premises "All P are Q", "Some R are P", and "No R are S", which conclusion is valid?

A Some R are Q B All S are Q C No P are S D Some Q are not S

Why: Since all P are Q and some R are P, some R are Q. No direct conclusion about S follows.

Question 234

Question bank

Given the premises: "All M are N", "No N are O", and "Some O are P", which conclusion is valid?

A No M are O B Some P are N C All O are M D Some N are P

Why: Since no N are O and all M are N, no M can be O.

Question 235

Question bank

If the premises are: "Some A are B", "All B are C", and "No C are D", which conclusion is valid?

A Some A are not D B All A are D C No B are D D Some D are A

Why: Since no C are D and all B are C, no B are D, so some A (which are B) are not D.

Question 236

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Refer to the diagram below. Given the premises "All X are Y", "Some Z are X", and "No Z are W", which conclusion is valid?

A Some Z are Y B All W are X C No Y are Z D Some W are X

Why: Since all X are Y and some Z are X, some Z are Y. No direct conclusion about W follows.

Question 237

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In a certain group of 237 individuals, the following statements are true: (1) All engineers are mathematicians. (2) Some mathematicians are physicists. (3) No physicist is a chemist. (4) Some chemists are engineers. Based on these statements, which of the following conclusions logically follows?

A Some engineers are not physicists. B All chemists are mathematicians. C No engineer is a physicist. D Some physicists are engineers.

Why: Step 1: From (1), all engineers are mathematicians. So, engineers ⊆ mathematicians. Step 2: From (2), some mathematicians are physicists, so mathematicians ∩ physicists ≠ ∅. Step 3: From (3), no physicist is a chemist, so physicists ∩ chemists = ∅. Step 4: From (4), some chemists are engineers, so chemists ∩ engineers ≠ ∅. Step 5: Since chemists ∩ engineers ≠ ∅ and all engineers ⊆ mathematicians, some chemists are mathematicians. Step 6: But no physicist is a chemist, so physicists and chemists are disjoint. Step 7: Since some engineers are chemists and no physicist is a chemist, those engineers who are chemists cannot be physicists. Step 8: Also, since all engineers are mathematicians and some mathematicians are physicists, it is possible that some engineers are physicists, but the chemist-engineers cannot be physicists. Step 9: Therefore, no engineer is a physicist is too strong a statement; however, since some engineers are chemists and no chemist is a physicist, some engineers are definitely not physicists. Step 10: But option A says 'Some engineers are not physicists' which is true but trivial; option C says 'No engineer is a physicist' which contradicts the possibility that some mathematicians are physicists and all engineers are mathematicians. Step 11: However, since some chemists are engineers and no physicist is a chemist, the engineers who are chemists cannot be physicists. Step 12: But the question asks which logically follows. The only conclusion that must be true is that no engineer is a physicist because if any engineer were a physicist, that engineer would also be a chemist (from (4)), which contradicts (3). Hence, option C is correct.

Question 238

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Given the premises: (i) Some A are B. (ii) All B are C. (iii) No C are D. (iv) Some D are E. Which of the following conclusions is definitely false?

A Some A are not D. B Some E are not C. C All A are E. D No B is D.

Why: Step 1: From (i) Some A are B. Step 2: From (ii) All B are C, so B ⊆ C. Step 3: From (iii) No C are D, so C ∩ D = ∅. Step 4: From (iv) Some D are E, so D ∩ E ≠ ∅. Step 5: Since B ⊆ C and C ∩ D = ∅, B ∩ D = ∅. Step 6: Since some A are B, and B ∩ D = ∅, some A are not D. Step 7: Some E are not C is true because E overlaps with D and D is disjoint with C. Step 8: No B is D is true because B ⊆ C and C ∩ D = ∅. Step 9: All A are E is false because only some A are B and B is disjoint from D and E is connected to D. Step 10: Therefore, 'All A are E' is definitely false.

Question 239

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Consider the following statements: (1) No P is Q. (2) Some Q are R. (3) All R are S. (4) Some S are not P. Which of the following must be true?

A Some R are not P. B No S is P. C Some Q are not S. D All P are not R.

Why: Step 1: From (1), P ∩ Q = ∅. Step 2: From (2), Q ∩ R ≠ ∅. Step 3: From (3), R ⊆ S. Step 4: From (4), some S are not P. Step 5: Since some Q are R and R are S, some Q are S. Step 6: Since P and Q are disjoint, P and R are disjoint (because R ⊆ S and Q ∩ R ≠ ∅ but P ∩ Q = ∅). Step 7: Therefore, some R are not P (because R is subset of S and some S are not P). Step 8: Option B says no S is P, which is too strong; only some S are not P. Step 9: Option C says some Q are not S, which contradicts Q ∩ R ≠ ∅ and R ⊆ S. Step 10: Option D says all P are not R, which cannot be concluded definitively. Hence, option A is correct.

Question 240

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In a population of 349 people, the following are known: (i) All members of group X are in group Y. (ii) Some members of group Y are in group Z. (iii) No member of group Z is in group W. (iv) Some members of group W are in group X. Which of the following statements is logically consistent with the above?

A Some members of group X are in group Z. B No member of group Y is in group W. C Some members of group W are not in group Z. D All members of group W are in group Y.

Why: Step 1: From (i), X ⊆ Y. Step 2: From (ii), some Y ∩ Z ≠ ∅. Step 3: From (iii), Z ∩ W = ∅. Step 4: From (iv), some W ∩ X ≠ ∅. Step 5: Since X ⊆ Y, some W ∩ Y ≠ ∅. Step 6: Since Z ∩ W = ∅, W members cannot be in Z. Step 7: Therefore, some W are not in Z is true. Step 8: Option A is false because if some X were in Z, then since X ⊆ Y, some Y would be in Z, which is true, but since W intersects X and Z and W are disjoint, it contradicts. Step 9: Option B is false because some W intersect X and X ⊆ Y, so some Y are in W. Step 10: Option D is false because W may have members outside Y. Hence, option C is correct.

Question 241

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Given the premises: (1) All M are N. (2) Some N are O. (3) No O are P. (4) Some P are Q. Which of the following conclusions is valid?

A Some M are not P. B All Q are not O. C Some N are not Q. D No M is Q.

Why: Step 1: From (1), M ⊆ N. Step 2: From (2), some N ∩ O ≠ ∅. Step 3: From (3), O ∩ P = ∅. Step 4: From (4), some P ∩ Q ≠ ∅. Step 5: Since O and P are disjoint, and some N are O, some N are not P. Step 6: Since M ⊆ N, some M are not P. Step 7: Option B is false because Q may or may not overlap with O. Step 8: Option C is not necessarily true; some N could be Q. Step 9: Option D is not necessarily true; M could overlap with Q. Hence, option A is valid.

Question 242

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Consider the statements: (i) Some X are Y. (ii) All Y are Z. (iii) No Z are W. (iv) Some W are X. Which of the following is a contradiction?

A Some X are not W. B Some Y are not W. C All X are Z. D No X is W.

Why: Step 1: From (i), some X ∩ Y ≠ ∅. Step 2: From (ii), Y ⊆ Z. Step 3: From (iii), Z ∩ W = ∅. Step 4: From (iv), some W ∩ X ≠ ∅. Step 5: Since Y ⊆ Z and Z ∩ W = ∅, Y ∩ W = ∅. Step 6: Some X are Y, so those X are in Z and cannot be in W. Step 7: But some W are X, so some X are in W. Step 8: Therefore, all X are Z is false because some X are in W, which is disjoint from Z. Step 9: Option C contradicts the premises. Hence, option C is a contradiction.

Question 243

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In a set of 421 students, the following are true: (1) All who study Physics also study Mathematics. (2) Some who study Mathematics study Chemistry. (3) No student studying Chemistry studies Biology. (4) Some students studying Biology study Physics. Which of the following statements is logically impossible?

A Some students study both Physics and Biology. B All students studying Biology study Mathematics. C Some students study both Chemistry and Physics. D No student studies both Chemistry and Biology.

Why: Step 1: From (1), Physics ⊆ Mathematics. Step 2: From (2), some Mathematics ∩ Chemistry ≠ ∅. Step 3: From (3), Chemistry ∩ Biology = ∅. Step 4: From (4), some Biology ∩ Physics ≠ ∅. Step 5: Since Physics ⊆ Mathematics, Biology ∩ Physics ⊆ Biology ∩ Mathematics. Step 6: Since Chemistry and Biology are disjoint, and some Mathematics are Chemistry, some Mathematics are not Biology. Step 7: Some students study both Chemistry and Physics would mean Chemistry ∩ Physics ≠ ∅. Step 8: But Physics ⊆ Mathematics and Chemistry ∩ Biology = ∅, so Chemistry and Physics can overlap only if Chemistry and Mathematics overlap. Step 9: However, since Biology and Chemistry are disjoint and some Biology study Physics, the students studying both Chemistry and Physics would contradict the disjointness. Step 10: Hence, option C is impossible.

Question 244

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Given the premises: (i) Some A are B. (ii) All B are C. (iii) Some C are not D. (iv) All D are E. Which of the following conclusions is logically valid?

A Some A are not E. B Some C are E. C All A are C. D Some D are not C.

Why: Step 1: From (i), some A ∩ B ≠ ∅. Step 2: From (ii), B ⊆ C. Step 3: So some A are B and B are C, so some A are C. Step 4: From (iii), some C are not D. Step 5: From (iv), D ⊆ E. Step 6: Since some C are not D, some C may or may not be E. Step 7: But since all D are E, and some C are D (because B ⊆ C and some B exist), some C are E. Step 8: Option A is false because some A are B and B are C, and D ⊆ E, so some A are E indirectly. Step 9: Option C is false because only some A are B, so not all A are C. Step 10: Option D is false because all D are E, but no info about D not being C. Hence, option B is valid.

Question 245

Question bank

In a survey of 512 people, the following facts are established: (1) All who like Jazz also like Blues. (2) Some who like Blues like Rock. (3) No one who likes Rock likes Classical. (4) Some who like Classical like Jazz. Which of the following is a logical inference?

A Some who like Classical also like Blues. B No one who likes Jazz likes Rock. C All who like Classical also like Blues. D Some who like Rock also like Jazz.

Why: Step 1: From (1), Jazz ⊆ Blues. Step 2: From (2), some Blues ∩ Rock ≠ ∅. Step 3: From (3), Rock ∩ Classical = ∅. Step 4: From (4), some Classical ∩ Jazz ≠ ∅. Step 5: Since Jazz ⊆ Blues, some Classical ∩ Blues ≠ ∅. Step 6: Option A states some Classical also like Blues, which is true. Step 7: Option B is false because Jazz ⊆ Blues and some Blues like Rock, so Jazz could like Rock. Step 8: Option C is false because only some Classical like Jazz. Step 9: Option D is false because Rock and Classical are disjoint. Hence, option A is correct.

Question 246

Question bank

Consider the following premises: (i) No S are T. (ii) Some T are U. (iii) All U are V. (iv) Some V are S. Which of the following conclusions is logically inconsistent?

A Some S are not U. B No U is S. C Some T are not V. D All S are V.

Why: Step 1: From (i), S ∩ T = ∅. Step 2: From (ii), some T ∩ U ≠ ∅. Step 3: From (iii), U ⊆ V. Step 4: From (iv), some V ∩ S ≠ ∅. Step 5: Since some V are S and U ⊆ V, some S may or may not be U. Step 6: Option A is consistent because some S may not be U. Step 7: Option B is consistent because no U is S can be true or false. Step 8: Option C is consistent because some T may not be V. Step 9: Option D says all S are V, which contradicts (i) and (iv) because if no S are T and some T are U and all U are V, then all S cannot be V. Hence, option D is inconsistent.

Question 247

Question bank

Given the following statements: (1) Some L are M. (2) All M are N. (3) No N are O. (4) Some O are P. Which of the following is a valid conclusion?

A Some L are not O. B All P are N. C No L is P. D Some M are not P.

Why: Step 1: From (1), some L ∩ M ≠ ∅. Step 2: From (2), M ⊆ N. Step 3: From (3), N ∩ O = ∅. Step 4: From (4), some O ∩ P ≠ ∅. Step 5: Since M ⊆ N and N ∩ O = ∅, M ∩ O = ∅. Step 6: Since some L are M and M ∩ O = ∅, some L are not O. Step 7: Option B is false because P and N are disjoint. Step 8: Option C cannot be concluded definitively. Step 9: Option D is true but not necessarily valid as some M may or may not be P. Hence, option A is valid.

Question 248

Question bank

In a group of 678 people, the following are true: (i) All who like Tea also like Coffee. (ii) Some who like Coffee like Juice. (iii) No one who likes Juice likes Soda. (iv) Some who like Soda like Tea. Which of the following statements is logically impossible?

A Some who like Soda also like Coffee. B All who like Soda also like Coffee. C Some who like Juice also like Tea. D No one who likes Tea likes Juice.

Why: Step 1: From (i), Tea ⊆ Coffee. Step 2: From (ii), some Coffee ∩ Juice ≠ ∅. Step 3: From (iii), Juice ∩ Soda = ∅. Step 4: From (iv), some Soda ∩ Tea ≠ ∅. Step 5: Since Tea ⊆ Coffee, some Soda ∩ Coffee ≠ ∅. Step 6: Option A is possible. Step 7: Option B says all Soda ⊆ Coffee, which is impossible because some Soda like Juice is disjoint. Step 8: Option C is possible because Tea ⊆ Coffee and some Coffee like Juice. Step 9: Option D is possible because Tea and Juice can be disjoint. Hence, option B is impossible.

Question 249

Question bank

Given the premises: (1) Some X are Y. (2) All Y are Z. (3) No Z are W. (4) Some W are X. Which of the following conclusions is logically valid?

A Some X are not Z. B No X is W. C Some W are not Z. D All W are not X.

Why: Step 1: From (1), some X ∩ Y ≠ ∅. Step 2: From (2), Y ⊆ Z. Step 3: So some X are Z. Step 4: From (3), Z ∩ W = ∅. Step 5: From (4), some W ∩ X ≠ ∅. Step 6: Since Z and W are disjoint, and some X are Z, some X are not Z. Step 7: Since W and Z are disjoint, some W are not Z. Step 8: Option C is valid. Step 9: Option A is true but less direct. Step 10: Option B is false because some W are X. Step 11: Option D is false because some W are X. Hence, option C is correct.

Question 250

Question bank

Consider the statements: (i) All A are B. (ii) Some B are C. (iii) No C are D. (iv) Some D are A. Which of the following is a contradiction?

A Some A are not C. B No A is D. C Some D are B. D All A are C.

Why: Step 1: From (i), A ⊆ B. Step 2: From (ii), some B ∩ C ≠ ∅. Step 3: From (iii), C ∩ D = ∅. Step 4: From (iv), some D ∩ A ≠ ∅. Step 5: Since A ⊆ B, some D ∩ B ≠ ∅. Step 6: Since C and D are disjoint, and some B are C, some B are not C. Step 7: Option A is true because some A may not be C. Step 8: Option B is false because some D are A. Step 9: Option C is true because some D are A and A ⊆ B. Step 10: Option D says all A are C, which contradicts (iii) and (iv) because some A are D and no C are D. Hence, option D is a contradiction.

Question 251

Question bank

In a class of 289 students, the following are true: (1) All who play Football also play Cricket. (2) Some who play Cricket play Basketball. (3) No one who plays Basketball plays Tennis. (4) Some who play Tennis play Football. Which of the following statements is logically impossible?

A Some who play Tennis also play Cricket. B All who play Tennis also play Cricket. C Some who play Basketball also play Football. D No one who plays Football plays Tennis.

Why: Step 1: From (1), Football ⊆ Cricket. Step 2: From (2), some Cricket ∩ Basketball ≠ ∅. Step 3: From (3), Basketball ∩ Tennis = ∅. Step 4: From (4), some Tennis ∩ Football ≠ ∅. Step 5: Since Football ⊆ Cricket, some Tennis ∩ Cricket ≠ ∅. Step 6: Option A is possible. Step 7: Option B says all Tennis ⊆ Cricket, which is impossible because Tennis overlaps with Football (subset of Cricket) but may have members outside Cricket. Step 8: Option C is possible because Football ⊆ Cricket and some Cricket play Basketball. Step 9: Option D is false because some Tennis play Football. Hence, option B is impossible.

Question 252

Question bank

Given: (i) Some X are Y. (ii) All Y are Z. (iii) No Z are W. (iv) Some W are X. Which of the following is a valid conclusion?

A Some X are not Z. B No X is W. C Some W are not Z. D All W are not X.

Why: Step 1: From (i), some X ∩ Y ≠ ∅. Step 2: From (ii), Y ⊆ Z. Step 3: So some X are Z. Step 4: From (iii), Z ∩ W = ∅. Step 5: From (iv), some W ∩ X ≠ ∅. Step 6: Since Z and W are disjoint, and some X are Z, some X are not Z. Step 7: Since W and Z are disjoint, some W are not Z. Step 8: Option C is valid. Step 9: Option A is true but less direct. Step 10: Option B is false because some W are X. Step 11: Option D is false because some W are X. Hence, option C is correct.

Question 253

Question bank

In a set of 415 people, the following are true: (1) All who like Apples also like Bananas. (2) Some who like Bananas like Cherries. (3) No one who likes Cherries likes Dates. (4) Some who like Dates like Apples. Which of the following is logically impossible?

A Some who like Dates also like Bananas. B All who like Dates also like Bananas. C Some who like Cherries also like Apples. D No one who likes Apples likes Dates.

Why: Step 1: From (1), Apples ⊆ Bananas. Step 2: From (2), some Bananas ∩ Cherries ≠ ∅. Step 3: From (3), Cherries ∩ Dates = ∅. Step 4: From (4), some Dates ∩ Apples ≠ ∅. Step 5: Since Apples ⊆ Bananas, some Dates ∩ Bananas ≠ ∅. Step 6: Option A is possible. Step 7: Option B says all Dates ⊆ Bananas, which is impossible because Dates overlap with Apples (subset of Bananas) but may have members outside Bananas. Step 8: Option C is possible because Apples ⊆ Bananas and some Bananas like Cherries. Step 9: Option D is possible because Apples and Dates overlap. Hence, option B is impossible.

Question 1

PYQ 4.0 marks

Explain what a syllogism is and describe the key components that make up a categorical syllogism. Provide an example to illustrate your explanation.

Try answering in your head first.

Model answer

A syllogism is a form of deductive reasoning that uses two statements (premises) to prove a third statement (conclusion) is true. It is a fundamental tool in logical analysis and reasoning aptitude tests.

The key components of a categorical syllogism are:

1. Major Premise: This is the first statement that contains the major term (predicate of the conclusion) and the middle term. It establishes a relationship between two categories.

2. Minor Premise: This is the second statement that contains the minor term (subject of the conclusion) and the middle term. It connects the subject to the middle term.

3. Conclusion: This is the third statement derived from the two premises. It establishes a relationship between the major and minor terms, excluding the middle term.

4. Middle Term: This term appears in both premises but not in the conclusion. It serves as the bridge connecting the major and minor terms.

There are four basic types of categorical statements that form the foundation of syllogism premises: Universal Affirmative ('All As are Bs'), Universal Negative ('No As are Bs'), Particular Affirmative ('Some As are Bs'), and Particular Negative ('Some As are not Bs').

Example: Consider the argument: 'All humans are mortal (Major Premise); I am a human (Minor Premise); therefore, I am mortal (Conclusion).' In this example, 'humans' is the middle term, 'mortal' is the major term, 'I' is the minor term, and the conclusion logically follows from the two premises. This demonstrates how a syllogism uses logical reasoning to derive a valid conclusion from established premises.

More: Comprehensive explanation of syllogism components with example

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Question 2

PYQ 5.0 marks

Describe the advanced strategies for solving complex syllogism questions that involve multiple premises. Explain how to approach such problems systematically.

Try answering in your head first.

Model answer

Advanced strategies for tackling complex syllogism questions involve a systematic and methodical approach to problem-solving. When dealing with multiple premises, it is essential to break down the problem into manageable components and apply logical rules consistently.

1. Break Down Complex Statements: The first step is to decompose complex statements into simpler, more manageable ones. This involves identifying the subject, predicate, and quantifiers (All, Some, No, Some not) in each statement. By simplifying the language, you can more easily identify the relationships between terms and apply syllogistic rules.

2. Create Combinations of Statements: When multiple premises are given, create logical combinations by linking statements through their common terms (middle terms). Identify which statements share terms and determine how they connect. This helps establish chains of reasoning that lead to valid conclusions.

3. Apply Rules Systematically: Use established syllogistic rules consistently throughout your analysis. Key rules include: the middle term must be distributed at least once, if a term is distributed in the conclusion it must be distributed in the premise, and from two negative premises no conclusion can be drawn. Applying these rules systematically ensures logical validity.

4. Start with Universal Statements: When analyzing multiple premises, it is often helpful to begin with Universal statements (All and No) before proceeding to Particular statements (Some and Some not). This approach can simplify the analysis by establishing broader categorical relationships first.

5. Practice with Varied Examples: Building problem-solving skills requires consistent practice with a variety of syllogism questions. Exposure to different question types, complexity levels, and statement combinations helps develop pattern recognition and intuition for identifying valid conclusions.

By combining these strategies and practicing regularly, you can develop the ability to solve even the most complex syllogism questions efficiently and accurately.

More: Comprehensive explanation of advanced syllogism strategies

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