In mathematics the complement of a set *X*, sometimes written *X*' or *X*^{c}, is the set of all the elements in the universe under consideration excluding those in the specified set. So if the current universe is the set of natural numbers and *X* is the set of even numbers then *X*' is the set of odd numbers.

In logic the complement of a proposition is the negation of that proposition. For example the complement of "the sun is shining" would be "the sun is not shining". For this reason the unary function in a Boolean algebra is often referred to as the complement operation.