Definition:Intersection of Relations/General Definition

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 $t \in T$:


 * $s \mathrel \RR t$ :
 * $\forall \QQ \in \mathscr R: s \mathrel \QQ t$

Also see

 * Definition:Union of Relations/General Definition