Definition:Union of Relations/General Definition
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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 $t \in T$:
- $s \mathrel \RR t$ if and only if for some $\QQ \in \mathscr R$, $s \mathrel \QQ t$