Syllogism — Test conclusions from: (A) All basketball players are tall men. (B) All basketball players are athletes. Conclusions: I) All tall men are basketball players. II) All athletes are basketball players.

Introduction / Context:
We are given two universal premises about 'basketball players': they are tall men and they are athletes. We must check whether conclusions about all tall men or all athletes being basketball players necessarily follow.

Given Data / Assumptions:

• A: BasketballPlayers ⊆ TallMen.
• B: BasketballPlayers ⊆ Athletes.
• No premise relating Athletes and TallMen directly, nor reversing subset relations.

Concept / Approach:
Universal statements of the form 'All X are Y' establish X ⊆ Y. Their converses ('All Y are X') are not valid without extra premises. Thus from X ⊆ Y we cannot conclude Y ⊆ X.

Step-by-Step Solution:

Verification / Alternative check:
Construct a model where many tall men are not players, and many athletes are not players; the premises still hold. Hence the conclusions fail in at least one model, so they do not logically follow.

Why Other Options Are Wrong:

• I alone can be drawn: converse error.
• II alone can be drawn: converse error.
• Both can be drawn: both are converses and invalid.

Common Pitfalls:
Assuming 'All X are Y' implies 'All Y are X'. It does not unless explicitly stated.

Final Answer:
Both cannot be drawn.