How to construct a symmetric, transitive and reflexive relation

Question

If R is a binary relation in a set X ≠∅ that is symmetric, transitive, then R is reflexive.

This is false and I have to change the argument to make it true. How can I do this? Thanks!

Answer 1

If for every $x\in X$ there is some $y\in X$ such that $xRy$, then $yRx$ because $R$ is symmetric. Then, $xRy$ and $yRx$, so $xRx$ since $R$· is transitive.

But the condition "for every $x\in X$ there is some $y\in X$ such that $xRy$" is essential.