Question

Give examples of relations which are reflexive and symmetric but not transitive

Answer 1

For a relation $R$ defined as

$R=\left\{\right(1,1),(2,2),(1,2),(2,1)\}$

as $(1,1);(2,2)$lies in $R$, $R$ is symmetric

as $(1,2);(2,1)$lies in $R$, $R$ is reflexive

so $R$ is reflexive and symmetric but not transitive.