Statement and Conclusions

In Statements and Conclusions problems, you are given a statement (a factual sentence), followed by one or more conclusions. Your task is to analyze whether these conclusions logically follow from the given statement(s).

This topic tests your ability to interpret information carefully and apply logical reasoning to judge the validity of conclusions.

What is a Statement?

  • A statement is a sentence that conveys some information or fact.
  • It can be true, false, or uncertain.
  • In reasoning problems, the statement is assumed to be true for the sake of analysis, even if it might not be true in reality.

What is a Conclusion?

  • A conclusion is a judgment or inference drawn from the statement.

  • It may be:

    • Definitely true (must follow logically from the statement),
    • Definitely false (contradicts the statement),
    • Or Cannot be determined (may be true or false, no definite inference).

Key Rules to Judge Conclusions

ScenarioConclusion Status
Conclusion directly supported by statementFollows (True)
Conclusion contradicts statementDoes not follow (False)
Conclusion is unrelated or insufficient informationCan’t say (Indeterminate)

Types of Statements Commonly Seen

  • Universal statements:

    • "All students are hard-working."

  • Particular statements:

    • "Some birds can fly."

  • Negative statements:

    • "No dogs are cats."

  • Conditional statements:

    • "If it rains, the ground gets wet."

How to Approach These Questions

  1. Read the statement carefully, assume it to be true.
  2. Analyze each conclusion separately.
  3. Check if the conclusion is supported or contradicted by the statement.
  4. If insufficient data is available, mark the conclusion as Cannot be determined.

Conceptual Tips and Common Mistakes

  • Don’t bring in outside knowledge; rely only on the information given.
  • Distinguish between “Some” and “All”.
  • Beware of absolute conclusions if statement only says “Some”.
  • Pay attention to negations like “No” or “Not”.
  • Don’t confuse “Could be true” with “Must be true”.

Examples

Example 1

Statement:
All cats are animals.

Conclusions:

  1. All animals are cats.
  2. Some animals are cats.
  3. No cat is an animal.

Analysis:

  • Conclusion 1: Does not follow (All cats are animals ≠ all animals are cats).
  • Conclusion 2: Follows (If all cats are animals, some animals definitely are cats).
  • Conclusion 3: Does not follow (contradicts statement).

Example 2

Statement:
Some birds are sparrows.

Conclusions:

  1. Some sparrows are birds.
  2. All birds are sparrows.
  3. Some birds are not sparrows.

Analysis:

  • Conclusion 1: Follows (If some birds are sparrows, then some sparrows are birds).
  • Conclusion 2: Does not follow (statement says only some, not all).
  • Conclusion 3: Can’t say (statement doesn’t specify about other birds).

Example 3

Statement:
No dogs are cats.

Conclusions:

  1. No cats are dogs.
  2. Some dogs are cats.
  3. Some cats are not dogs.

Analysis:

  • Conclusion 1: Follows (logical conversion of “No dogs are cats”).
  • Conclusion 2: Does not follow (contradicts statement).
  • Conclusion 3: Follows (if no cats are dogs, some cats must not be dogs).

Example 4

Statement:
If it rains, the ground gets wet.

Conclusions:

  1. It rains only if the ground gets wet.
  2. The ground gets wet only if it rains.
  3. If the ground is not wet, it did not rain.

Analysis:

  • Conclusion 1: Does not follow (statement is not bi-conditional).
  • Conclusion 2: Does not follow (other reasons may cause wet ground).
  • Conclusion 3: Follows (contrapositive).
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