Answer to Question #338302 in Discrete Mathematics for Muhammad Omer

Question

. State the converse, contrapositive, and inverse of each of these conditional statements. A positive integer is a prime only if it has no divisors other than 1 and itself.

Answer 1

If implication is $p \rightarrow q$

Then

Inverse $\neg p\rightarrow \neg q$

Converse $q\rightarrow p$

Contrapositive $\neg q \rightarrow \neg p$

p: It has no divisors other than 1 and itself.

q: A positive integer is a prime.

$\neg p$ It has divisors other than 1 and itself.

$\neg q$ A positive integer is not a prime.

Inverse

A positive integer is not a prime if it has divisors other than 1 and itself.

Converse

If a positive integer is a prime then it has no divisors other than 1 and itself.

Contrapositive

If a positive integer is not a prime then it has divisors other than 1 and itself.