Syllogism test on athletes: from 'All good athletes win' and 'All good athletes eat well', decide which conclusions must follow (All who eat well are good athletes; All who win eat well)
Verbal Reasoning
Logical Deduction
Difficulty: Medium
Choose an option
Answer
Correct Answer: Neither I nor II follows
Explanation
Given data
- Premise 1: All good athletes win (GoodAthlete ⟶ Win).
- Premise 2: All good athletes eat well (GoodAthlete ⟶ EatWell).
- Conclusions to test:
- I: All who eat well are good athletes (EatWell ⟶ GoodAthlete).
- II: All who win eat well (Win ⟶ EatWell).
Concept/Approach (why this method)
Chain only what is compelled by universals. Beware of illicit converse: from 'All A are B' you cannot infer 'All B are A'.
Step-by-Step calculation / logic1) From premises: GoodAthlete ⟶ Win and GoodAthlete ⟶ EatWell, hence GoodAthlete ⟶ (Win ∧ EatWell).2) Conclusion I flips Premise 2 (illicit converse), not guaranteed ⇒ false.3) Conclusion II extends 'Win' to everyone, but we only know a subset (good athletes) who win eat well ⇒ not necessary ⇒ false.
Verification/Alternative
Counterexample: Let some non-athletes eat well or win; premises permit this. Then I and II fail.
Common pitfalls
- Assuming all winners are good athletes (overgeneralization).
- Conflating sufficient and necessary conditions.
Final AnswerNeither I nor II follows.