\begin{definition}[Definition:Relative Complement]
Let $S$ be a set, and let $T \subseteq S$, that is: let $T$ be a subset of $S$.
Then the set difference $S \setminus T$ can be written $\relcomp S T$, and is called the '''relative complement of $T$ in $S$''', or the '''complement of $T$ relative to $S$'''.
Thus:
:$\relcomp S T = \set {x \in S : x \notin T}$
\end{definition}