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.