Definition:Union of Relations

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

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

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


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

where $\cup$ denotes set union.

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


 * $s \mathrel \QQ t$ $s \mathrel {\RR_1} t$ or $s \mathrel {\RR_2} t$

Also see

 * Union of Relations is Relation
 * Definition:Intersection of Relations
 * Definition:Union Mapping