## 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.