Definition:Union of Relations/General Definition

Definition
Let $S$ and $T$ be sets. Let $\mathscr R$ be a collection of relations on $S \times T$.

The union of $\mathscr R$ is the relation $\RR$ defined by:


 * $\ds \RR = \bigcup \mathscr R$

where $\bigcup$ denotes set union.

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


 * $s \mathrel \RR t$ for some $\QQ \in \mathscr R$, $s \mathrel \QQ t$

Also see

 * Definition:Intersection of Relations/General Definition