Question

The statement p → q represents "If a number is doubled, the result is even.”

Which represents the inverse?

Answer 1

The inverse of an implication p ⇒ q is ¬p ⇒ ¬q (where ¬ means "not", denoting the logical negation).

Compare this to the converse and contrapositive of p ⇒ q.

Converse: q ⇒ p

Contrapositive: ¬q ⇒ ¬p

(in other words, the contrapositive is the inverse of the converse)

Then the inverse of the given statement is

"If a number is not doubled, then the result is not even."