A relation $\mathcal{R}$ on a set $A$ is reflexive if and only if $a\mathcal{R}a$ 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 reflexive because 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.