Reflexive relation

A relation $R$ on $X$ is reflexive when $xRx$ for every $x\in X$.

The reflexive closure of a binary relation $R\subseteq A\times A$ is $R\cup {\Delta }_A$, where ${\Delta }_A=\{(a,a):a\in A\}$. Every reflexive relation containing $R$ must contain the diagonal, so this is the least such extension.