For integers m and n, each exceeding 1, let the statements be: P: m is a divisor of n, Q: m is a divisor of n², and R: m is a prime number. Which of the following implications is true?

Question

Accepted Answer

Q ∧ R → P. If m is prime and m divides n^2, then a prime dividing a square must divide the base, so m divides n. Thus Q ^ R -> P is the valid implication; the others fail (e.g. m=4,n=2 breaks Q->P).

For integers m and n, each exceeding 1, let the statements be: P: m is a divisor of n, Q: m is a divisor of n², and R: m is a prime number. Which of the following implications is true?

Solution

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