It is given that either is prime or is divisible by 3, that if is prime then is odd, and that is even. Which of the following must be true?
Answer and explanation
Correct answer: A. is divisible by 3
- Step 1: Let : prime, : divisible by 3, : odd. We have , and .
- Step 2: From and , follows. Then gives : is divisible by .
Answer
is divisible by 3.
Why not the others: 'Prime' and 'prime and divisible by 3' contradict ; 'not divisible by 3' contradicts ; 'odd' contradicts the given fact. (An example is .)
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