$(10$ points$)$ Indifference relation

Suppose $x$ is a set and $$ is a complete and transitive preference relation on $x.$ Recall that

we can derive the indifference binary relation $$ on $x$ from $$ as

$xyLongleftrightarrow(xy$ and $yx).$

Show that the relation $$ on $x$ is an equivalence relation.

Note that a binary relation $R$ on $x$ is an equivalence relation if it is reflexive, symmetric, and

transitive.