\begin{definition}[Definition:Set Complement]
The '''set complement''' (or, when the context is established, just '''complement''') of a set $S$ in a universe $\mathbb U$ is defined as:
:$\map \complement S = \relcomp {\mathbb U} S = \mathbb U \setminus S$
See the definition of Relative Complement for the definition of $\relcomp {\mathbb U} S$.
Thus the complement of a set $S$ is the '''relative complement of $S$ in the universe''', or the '''complement of $S$ relative to the universe'''.
A common alternative to the symbology $\map \complement S$, which we will sometimes use, is $\overline S$.
\end{definition}