Question

What are the inverse of the conditional statement “ A positive integer is a composite only if it has  divisors other than 1 and itself.”

(a) “A positive integer is a composite if it has divisors other than 1 and itself.”

(b) “If a positive integer has no divisors other than 1 and itself, then it is not composite.”

(c) “If a positive integer is not composite, then it has no divisors other than 1 and itself.”

(d) None of the mentioned

The question was posed to me in an interview.

My enquiry is from Logics in chapter The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

The correct choice is (c) “If a positive integer is not composite, then it has no divisors other than 1 and itself.”

For explanation I would say: p only if q has inverse ¬p → ¬q.