Question

Statements:
I. No athletes are vegetarians.
II. All players are athletes.
III. Therefore, \dots

• A. no players are vegetarians
• B. all players are vegetarian
• C. some players are vegetarian
• D. all vegetarians are players

Hint:

If $P\subseteq A$ and $A$ has no overlap with $V$, then $P$ also has no overlap with $V$.

Answer 1

The Correct Option is A

Let $A=$ athletes,\ $P=$ players,\ $V=$ vegetarians.
I: $A \cap V=\varnothing$ (no athlete is a vegetarian).
II: $P \subseteq A$ (all players are athletes).
Then $P \subseteq A$ together with $A \cap V=\varnothing$ implies $P \cap V=\varnothing$.
Hence, no players are vegetarians \Rightarrow option (a).