## Problem-21

**Problem-21**

State the converse, contrapositive, and inverse of each of these conditional statements.

**a) **If it snows tonight, then I will stay at home.

**b)** I come to class whenever there is going to be a quiz.

**c)** A positive integer is a prime only if it has no divisors other than 1 and itself.

**Solution**

**a) **If it snows tonight, then I will stay at home.

Converse: If I stay home, then it will snow tonight.

Contrapositive: If I do not stay at home, then it will not snow tonight.

Inverse: If it does not snow tonight, then I will not stay home.

**b)** I come to class whenever there is going to be a quiz.

Converse: If I come to class, then there will be a quiz.

Contrapositive: If I do not come to class, then there will not be a quiz.

Inverse: If there is not going to be a quiz, then I do not come to class.

**c)** A positive integer is a prime only if it has no divisors other than 1 and itself.

Converse: A positive integer is a prime if it has no divisors other than 1 and itself.

Contrapositive: If a positive integer has a divisor other than 1 and itself, then it is not prime.

Inverse: If a positive integer is not prime, then it has a divisor other than 1 and itself.