Converse

Definition

Let $p$ and $q$ be propositions. The converse of the implication $p \to q$ is the implication $q \to p$.

Remarks

An implication and its converse are not logically equivalent. For example, "if $n = 2$, then $n$ is prime" is true, but its converse "if $n$ is prime, then $n = 2$" is false. The inverse of $p \to q$ is $\neg p \to \neg q$. It is the contrapositive of the converse.

Explanations

L1 human

The converse reads the arrow backwards. "If an animal is a dog, then it is a mammal" is true. Its converse, "if an animal is a mammal, then it is a dog", is false.