Answer to Question #178166 in Discrete Mathematics for Elaine

Question

III. State the converse, inverse, and contrapositive of each of the given statements.

1. If it snows tonight, I will stay home.
2. I go to the beach whenever it is a sunny summer day.
3. A positive integer is prime only if it has no divisors other than 1 and itself.

Answer 1

Solution:

(1): If it snows tonight, I will stay home.

Converse: If I will stay home, it snows tonight.

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

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

(2): I go to the beach whenever it is a sunny summer day.

Converse: It is a sunny summer day whenever I go to the beach.

Inverse: I do not go to the beach whenever it is not a sunny summer day.

Contrapositive: Whenever it is not a sunny summer day, I do not go to the beach.

(3): A positive integer is prime only if it has no divisors other than 1 and itself.

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

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

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