\begin{definition}[Definition:Complement of Relation]
Let $\RR \subseteq S \times T$ be a relation.
The '''complement of $\RR$''' is the relative complement of $\RR$ with respect to $S \times T$:
:$\relcomp {S \times T} \RR := \set {\tuple {s, t} \in S \times T: \tuple {s, t} \notin \RR}$
If the sets $S$ and $T$ are implicit, then $\map \complement \RR$ can be used.
\end{definition}