# Inverse (logic)

In traditional logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. Any conditional sentence has an inverse: the contrapositive of the converse. The inverse of $P \rightarrow Q$ is thus $\neg P \rightarrow \neg Q$.
The inverse of the inverse, that is, the inverse of $\neg P \rightarrow \neg Q$, is $\neg \neg P \rightarrow \neg \neg Q$. Since a double negation has no logical effect, the inverse of the inverse is logically equivalent to the original conditional $P \rightarrow Q$. Thus it is permissible to say that $\neg P \rightarrow \neg Q$ and $P \rightarrow Q$ are inverses of each other. Likewise, we may say that $P \rightarrow \neg Q$ and $\neg P \rightarrow Q$ are inverses of each other.