Definition:Extension of Relation

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This page is about extensions of relations. For other uses, see Extension.



$\RR_1 \subseteq X \times Y$ be a relation on $X \times Y$
$\RR_2 \subseteq S \times T$ be a relation on $S \times T$
$X \subseteq S$
$Y \subseteq T$
$\RR_2 \restriction_{X \times Y}$ be the restriction of $\RR_2$ to $X \times Y$.

Let $\RR_2 \restriction_{X \times Y} = \RR_1$.

Then $\RR_2$ extends or is an extension of $\RR_1$.

Also see