Question

Which is the contrapositive of the conditional statement?

If an animal is a turkey, then it has a beak.

A.
If an animal does not have a beak, then it is not a turkey.

B.
If an animal does not have a beak, then it is a turkey.

C.
If an animal has a beak, then it is a turkey.

D.
If an animal is not a turkey, then it is does not have a beak.

Answer 1

Given an if-then statement "if p, then q", we can create three related statements:

A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause. For instance, “If it rains, then they cancel school.”
"It rains" is the hypothesis.
"They cancel school" is the conclusion.

To form the converse of the conditional statement, interchange the hypothesis and the conclusion.
The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains."

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.
The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain."