# Complement (set theory)

From Citizendium

In set theory, the **complement** of a subset of a given set is the "remainder" of the larger set.

Formally, if *A* is a subset of *X* then the (relative) complement of *A* in *X* is

In some version of set theory it is common to postulate a "universal set" and restrict attention only to sets which are contained in this universe. We may then define the (absolute) complement

The relation of complementation to the other set-theoretic functions is given by *De Morgan's laws*: