Definition:Intersection of Relations

Definition
Let $S$ and $T$ be sets.

Let $\RR_1$ and $\RR_2$ be relations on $S \times T$.

The intersection of $\RR_1$ and $\RR_2$ is the relation $\QQ$ defined by:


 * $\QQ := \RR_1 \cap \RR_2$

where $\cap$ denotes set intersection.

Explicitly, for $s \in S$ and $t \in T$, we have:


 * $s \mathrel \QQ t$ both $s \mathrel{\RR_1} t$ and $s \mathrel{\RR_2} t$

Also see

 * Union of Relations