27  Statements and Conclusions

27.1 Introduction

This type of reasoning problem asks whether a given conclusion logically follows from the provided statement(s).
Unlike assumptions, conclusions are explicit deductions drawn from the statement, not background beliefs.

27.2 1) Key Concepts

27.2.1 1.1 Statement

A piece of information or fact provided in the question.

27.2.2 1.2 Conclusion

An inference that must follow from the given statement(s), without adding external knowledge.

27.3 2) How to Approach

  1. Read the statement carefully.
  2. Identify the scope — avoid adding outside knowledge.
  3. Test each conclusion: Is it definitely true, definitely false, or not certain?
  4. In exams, conclusions are tested as “follows” or “does not follow.”

27.4 3) Examples

27.4.1 Example 1

Statement: All students in the class are intelligent.
Conclusions:
1. Some students are intelligent.
2. No student in the class is dull.

Answer: Both conclusions follow.

27.4.2 Example 2

Statement: Some doctors are teachers.
Conclusions:
1. Some teachers are doctors.
2. All teachers are doctors.

Answer: (1) follows (conversion of “some”); (2) does not follow.

27.4.3 Example 3

Statement: All engineers are hardworking.
Conclusions:
1. No engineer is lazy.
2. Some hardworking people are engineers.

Answer: Both follow.

27.4.4 Example 4

Statement: Some cats are dogs.
Conclusions:
1. Some dogs are cats.
2. All dogs are cats.

Answer: (1) follows, (2) does not.

27.4.5 Example 5

Statement: All apples are fruits. All fruits are perishable.
Conclusions:
1. All apples are perishable.
2. All perishable things are apples.

Answer: (1) follows (universal conclusion). (2) does not follow.

27.5 4) Golden Rules

  • “All A are B” ⇒ “Some A are B” follows, but not “All B are A.”
  • “Some A are B” ⇒ implies existence, but not universality.
  • Negative conclusions require explicit negatives in the statement.
  • Avoid assumptions from real-world knowledge (e.g., “All doctors are rich”).
  • Diagram (Venn/Set) method helps visualize.

27.6 5) Practice Questions

  1. Statement: All books are novels. Some novels are poems.
    Conclusions:
    1. Some poems are books.
    2. Some novels are books.
  2. Statement: Some politicians are honest.
    Conclusions:
    1. Some honest people are politicians.
    2. All politicians are honest.
  3. Statement: All trains are vehicles. Some vehicles are buses.
    Conclusions:
    1. Some buses are trains.
    2. Some vehicles are trains.
  4. Statement: No teacher is careless. All students are careful.
    Conclusions:
    1. No student is a teacher.
    2. Some teachers are careful.
  5. Statement: All dogs are animals. Some animals are cats.
    Conclusions:
    1. Some cats are dogs.
    2. Some animals are dogs.

27.7 6) Answer Key

    1. does not follow; (b) follows.
    1. follows; (b) does not follow.
    1. does not follow; (b) follows.
    1. cannot be concluded; (b) follows.
    1. does not follow; (b) follows.

27.8 7) Summary

  • Statements → fixed facts; conclusions → testable inferences.
  • Use Venn diagrams or logical rules (all/some/no).
  • Do not bring real-world facts. Stick strictly to the given statement.
  • Remember: Some ≠ All, and All does not imply only.
  • Correct identification comes with consistent practice.