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Statement and Conclusions

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Introduction to Statement and Conclusions

In logical reasoning tests, you will often encounter questions that present a statement followed by one or more conclusions. Your task is to decide whether these conclusions logically follow from the statement. This skill is crucial because it tests your ability to think clearly and critically, without making assumptions beyond the information given.

What is a Statement? A statement is a sentence that conveys a fact, opinion, or assumption. It provides information that we analyze to draw conclusions.

What is a Conclusion? A conclusion is a judgment or decision that is drawn based on the information in the statement. It should logically follow from the statement without adding extra information.

For example, consider the statement: "All students in the class passed the exam." A possible conclusion could be: "Some students passed the exam." This conclusion logically follows because if all students passed, then certainly some did.

However, a conclusion like "No student failed the exam." also follows logically because it is the opposite way of saying all passed. But a conclusion such as "Only the top students passed." does not follow because the statement does not specify anything about "top" students.

In this chapter, you will learn how to evaluate such conclusions carefully and systematically.

Types of Statements and Conclusions

Before we evaluate conclusions, it is important to understand the different types of statements and conclusions you may encounter.

Comparison of Statement and Conclusion Types
Type Description Example Statement Example Conclusion Validity
Factual Statement States a fact that can be verified All cars in the parking lot are red. Some cars in the parking lot are red. Definite Conclusion
Opinion Statement Expresses a personal belief or feeling Chocolate ice cream is the best flavor. Everyone likes chocolate ice cream. Invalid Conclusion
Assumption Unstated premise taken for granted He did not come to class today. He is sick. Possible Conclusion (not definite)
Definite Conclusion Must logically follow from the statement All birds can fly. Some birds can fly. Definite Conclusion
Possible Conclusion May or may not be true based on the statement Some students are absent today. All students are absent. Possible but not definite
Invalid Conclusion Does not logically follow from the statement All fruits are sweet. All sweet things are fruits. Invalid Conclusion

Evaluating Conclusions

To decide whether a conclusion follows logically from a statement, you can use several reasoning techniques. These help you avoid common traps and ensure your answers are accurate.

graph TD    A[Read the Statement Carefully] --> B[Understand the Meaning]    B --> C{Is the Conclusion Directly Supported?}    C -- Yes --> D[Conclusion is Definite]    C -- No --> E{Is the Conclusion Possibly True?}    E -- Yes --> F[Conclusion is Possible]    E -- No --> G[Conclusion is Invalid]    D --> H[Mark as Correct]    F --> H    G --> I[Discard Conclusion]

Step 1: Read the statement carefully and understand exactly what it says.

Step 2: Check if the conclusion is directly supported by the statement - this means it must be true in all cases.

Step 3: If not definite, check if the conclusion could possibly be true based on the statement.

Step 4: If neither definite nor possible, the conclusion is invalid and should be rejected.

Step 5: Use the elimination method to discard conclusions that contradict the statement or add information not given.

Worked Examples

Example 1: Simple Definite Conclusion Easy
Statement: All mangoes are fruits.
Conclusion: Some fruits are mangoes.

Step 1: The statement says every mango is a fruit.

Step 2: The conclusion says some fruits are mangoes, which is the reverse but logically true because if all mangoes are fruits, then some fruits must be mangoes.

Step 3: Since the conclusion must be true based on the statement, it is a definite conclusion.

Answer: The conclusion definitely follows from the statement.

Example 2: Possible vs Definite Conclusion Medium
Statement: Some students in the class are left-handed.
Conclusions:
1. All students are left-handed.
2. Some students are not left-handed.

Step 1: The statement says only some students are left-handed, so not all.

Step 2: Conclusion 1 says all students are left-handed, which is not supported by the statement. So, it is invalid.

Step 3: Conclusion 2 says some students are not left-handed, which is possible because if only some are left-handed, the rest may not be.

Answer: Conclusion 1 is invalid; Conclusion 2 is a possible conclusion.

Example 3: Invalid Conclusion Medium
Statement: No dogs are cats.
Conclusion: Some cats are dogs.

Step 1: The statement clearly says dogs and cats are mutually exclusive.

Step 2: The conclusion says some cats are dogs, which contradicts the statement.

Answer: The conclusion is invalid and does not follow.

Example 4: Multiple Conclusions Hard
Statement: All teachers are educated. Some educated people are artists.
Conclusions:
1. Some teachers are artists.
2. All artists are educated.
3. Some educated people are teachers.

Step 1: From the statement, all teachers belong to the educated group.

Step 2: Some educated people are artists, but it does not say teachers are artists.

Step 3: Conclusion 1 says some teachers are artists - this is not supported, so invalid.

Step 4: Conclusion 2 says all artists are educated - the statement says only some educated are artists, not all artists are educated, so invalid.

Step 5: Conclusion 3 says some educated people are teachers - since all teachers are educated, some educated must be teachers. So, this conclusion is definite.

Answer: Only Conclusion 3 follows definitely.

Example 5: Complex Statement with Assumptions Hard
Statement: If it rains, the ground gets wet. It is raining now.
Conclusions:
1. The ground is wet.
2. It might not rain tomorrow.
3. If the ground is wet, it has rained.

Step 1: The statement is a conditional: rain causes wet ground.

Step 2: Conclusion 1 says the ground is wet now because it is raining - this follows definitely.

Step 3: Conclusion 2 is about tomorrow's weather, which is not related to the statement - possible but not definite.

Step 4: Conclusion 3 says if the ground is wet, it has rained - this is the reverse of the statement and may not be true (the ground could be wet for other reasons), so invalid.

Answer: Conclusion 1 is definite, Conclusion 2 is possible, Conclusion 3 is invalid.

Quick Tips for Evaluating Statements and Conclusions

  • Always base your conclusion strictly on the information given in the statement without adding assumptions.
  • Use the elimination method by discarding conclusions that contradict the statement or add extra information.
  • Look for keywords like all, some, none to understand the scope of the statement and conclusions.
  • Practice time management by quickly identifying definite conclusions first, then possible ones.
  • Convert complex statements into simpler paraphrases to better analyze the logical flow.

Tips & Tricks

Tip: Always base your conclusion strictly on the information given in the statement without adding assumptions.

When to use: When evaluating any conclusion to avoid errors from unwarranted assumptions.

Tip: Use the elimination method by discarding conclusions that contradict the statement or add extra information.

When to use: When multiple conclusions are given and you need to quickly identify invalid ones.

Tip: Look for keywords like "all", "some", "none" to understand the scope of the statement and conclusions.

When to use: When dealing with universal or particular statements to judge conclusion validity.

Tip: Practice time management by quickly identifying definite conclusions first, then possible ones.

When to use: During timed competitive exams to maximize accuracy and speed.

Tip: Convert complex statements into simpler paraphrases to better analyze the logical flow.

When to use: When statements are lengthy or complicated, to reduce confusion.

Common Mistakes to Avoid

❌ Assuming information not given in the statement to validate a conclusion.
✓ Evaluate conclusions strictly based on the given statement without adding external facts.
Why: Students often rely on their own knowledge or assumptions instead of the provided data.
❌ Confusing possible conclusions with definite conclusions.
✓ Distinguish between conclusions that must follow and those that may follow; only mark definite ones as correct.
Why: Misinterpretation of logical necessity versus possibility leads to errors.
❌ Ignoring negative qualifiers like "not" or "none" in statements and conclusions.
✓ Pay close attention to negations as they completely change the meaning and validity of conclusions.
Why: Neglecting negations causes incorrect acceptance or rejection of conclusions.
❌ Rushing through questions and missing subtle logical cues.
✓ Take a moment to carefully analyze the statement and each conclusion before deciding.
Why: Time pressure leads to careless mistakes in logical reasoning.
❌ Overcomplicating simple statements by reading too much into them.
✓ Keep interpretations straightforward and literal unless explicitly stated otherwise.
Why: Overthinking causes confusion and incorrect conclusions.
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