Reflexive and Symmetric Relations

For an arbitrary set $A$, let’s define some important types of relations on $A$.

Reflexive relation

A relation $R$ on $A$ is a reflexive relation if $(a,a)\in R$ for every element that is $a\in A$. If there is an element $b\in A$ so that $(b,b) \not\in R$, then $R$ is not a reflexive relation. Let’s take the set $M= \{\alpha, \beta, \gamma\}$ and consider the following relations:

$R_1$, $R_2$, $R_3$ ...