Diagonal Relation is Reflexive

The diagonal relation $\Delta_S$ on a set $S$ is a reflexive relation in $S$.
 $\, \displaystyle \forall x \in S: \,$ $\displaystyle \tuple {x, x}$ $\in$ $\displaystyle \Delta_S$ Definition of Diagonal Relation
So $\Delta_S$ is reflexive.
$\blacksquare$