Diagonal Relation is Reflexive

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Theorem

The diagonal relation $\Delta_S$ on a set $S$ is a reflexive relation in $S$.


Proof

\(\, \displaystyle \forall x \in S: \, \) \(\displaystyle \tuple {x, x}\) \(\in\) \(\displaystyle \Delta_S\) Definition of Diagonal Relation

So $\Delta_S$ is reflexive.

$\blacksquare$