TMUA Logic Drill · Equivalent Statements

Medium· Paper 2 Style

Which statement is equivalent to:

A number is prime only if it has exactly two positive factors.

A. If a number has exactly two positive factors, then it is prime. B. If a number is prime, then it has exactly two positive factors. C. A number is prime if and only if it has exactly two positive factors. D. If a number is not prime, then it has exactly two positive factors.

Correct answer: B

Solution: “P only if Q” means P ⇒ Q. Here P is “the number is prime” and Q is “it has exactly two positive factors”.