Question

What is the contrapositive of the following statement? If Pi, the cat, is content, she is purring. Select the best answer from the choices provided.
If Pi is purring, then she is content.
Pi is purring if she is content.
If Pi is not purring, then she is not content.
If Pi is not content, then she is not purring.

Answer 1

Answer: The third option: If Pi is not purring, then she is not content.

The contrapositive of a conditional statement, is defined as the conditional formed by negating both the consequent and the antecedent, and changing the directions of the conditional.

Using letters:

The contrapositive of the conditional "If p, the q" is "If  not q, then not p".

Using symbols:

The contrapositive of p ⇒ q is ~q ⇒ ~p.

Note that the statement and its contrapsotive are logically equivalent.

So, for the case of this question you have to negate both the consequent (tthe cat is not purring) and the antecedent ( Pi is not content) and reverse the direction of the conditional, to form:

If the Pi is not purring then she is not content.