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.
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AI alone can be drawn
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BBoth can be drawn
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CBoth cannot be drawn
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DII alone can be drawn
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ENone of these
Answer
Correct Answer: Both cannot be drawn
Explanation
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:
Step 1: From A, BasketballPlayers ⊆ TallMen; does not imply TallMen ⊆ BasketballPlayers.Step 2: From B, BasketballPlayers ⊆ Athletes; does not imply Athletes ⊆ BasketballPlayers.Step 3: Therefore, neither I nor II is forced by the premises.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.