# Definition:Logical Complement/Complementary Pair

## Definition

For any propositional formula $\mathbf A$, the set $\left\{{\mathbf A, \neg \mathbf A}\right\}$ is called a complementary pair of formulas.

## Also known as

In case $\mathbf A$ is an atom, $\left\{{\mathbf A, \neg \mathbf A}\right\}$ is called a complementary pair of literals for $\mathbf A$.

## Linguistic Note

The word complement comes from the idea of complete-ment, it being the thing needed to complete something else.

It is a common mistake to confuse the words complement and compliment. Usually the latter is mistakenly used when the former is meant.