It is given that some students play chess, and every student who plays chess also plays tennis. Which of the following must be true?
Answer and explanation
Correct answer: E. Some students play tennis
- Step 1: Let = students, = chess players, = tennis players. Some student is in , and every chess player is in .
- Step 2: That same student is in , so some student plays tennis. The other statements are not forced.
Answer
Some students play tennis.
Why not the others: The converse ('every tennis player plays chess') does not follow; 'some tennis players do not play chess' is possible but not forced; 'no chess player plays tennis' contradicts the facts; 'every student plays tennis' goes beyond them.
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