reflexive relation

A relation $ℛ$ on a set $A$is reflexive if and only if $aℛa$ for all $a\in A$.

For example, let $A=\{1,2,3\}$.Then $\{(1,1),(2,2),(3,3),(1,3),(3,2)\}$ is a reflexive relation on $A$,because it contains $(a,a)$ for all $a\in A$.However, $\{(1,1),(2,2),(2,3),(3,1)\}$ is not reflexivebecause it does not contain $(3,3)$.

On a finite set with $n$ elements there are $2^{n^2}$ relations,of which $2^{n^2-n}$ are reflexive.