The question contains some statements followed by some conclusions. Decide…

Concept

In categorical syllogisms, a universal statement of the form ‘All A are B’ only establishes that A is a subset of B. It never licenses the converse ‘All B are A’, and two separate statements of the form ‘All A are B’ and ‘All A are C’ do not by themselves establish any direct relationship between B and C.

Application

• P: All good athletes want to win — good athletes ⊆ want-to-win.

• Q: All good athletes eat well — good athletes ⊆ eat-well.

Conclusion I says everyone who eats well is a good athlete — that is the converse of Q (eat-well ⊆ good athletes), which P and Q never assert, so it does not follow.

Conclusion II says everyone who wants to win eats well — that would need a direct link between the want-to-win group and the eat-well group. Both groups are only known to contain the good athletes as a subset; nothing connects them to each other outside that subset, so this conclusion does not follow either.

Cross-check

A single counterexample rules out both: imagine a person who is not a good athlete, wants to win, but does not eat well. This person does not contradict P or Q (both statements are only about good athletes), yet directly falsifies conclusion II. Similarly, a person who eats well without being a good athlete falsifies conclusion I. So neither conclusion I nor II follows from the given statements.