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 $\QQ \in \mathscr R$, $s \mathrel \QQ t$


Also see