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)

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 / logic
1) 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 Answer
Neither I nor II follows.