\begin{definition}[Definition:Intersection of Relations/General Definition]
Let $S$ and $T$ be sets.
Let $\mathscr R$ be a collection of relations on $S \times T$.
The '''intersection of $\mathscr R$''' is the relation $\RR$ defined by:
:$\ds \RR = \bigcap \mathscr R$
where $\bigcap$ denotes set intersection.
Explicitly, for $s \in S$ and $t \in T$:
:$s \mathrel \RR t$ {{iff}}:
::$\forall \QQ \in \mathscr R: s \mathrel \QQ t$
\end{definition}