If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation…

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If $R$ is the largest equivalence relation on a set $A$ and $S$ is any relation on $A$, then:

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Largest equivalence on $A$ is $A\times A$ (universal relation), so every relation $S$ on $A$ satisfies $S\subseteq A\times A=R$.

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