Definition:Intersection of Relations

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

Let $\mathcal R_1$ and $\mathcal R_2$ be relations on $S \times T$.

The intersection of $\mathcal R_1$ and $\mathcal R_2$ is the relation $\mathcal Q$ defined by:


 * $\mathcal Q := \mathcal R_1 \cap \mathcal R_2$

where $\cap$ denotes set intersection.

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


 * $s \mathrel{\mathcal Q} t$ iff both $s \mathrel{\mathcal R_1} t$ and $s \mathrel{\mathcal R_2} t$

Also see

 * Union of Relations