Question

Symmetric and transitive but not reflexive.

Answer 1

Let $A=\{-5,-6\}$.
Define a relation $R$ on $A$ as:
$R=\left\{\right(-5,-6),(-6,-5),(-5,-5\left)\right\}$
Relation $R$ is not reflexive as $(-6,-6)\notin R$
Relation $R$ is symmetric as $(-5,-6)\in R$ and $(-6,-5)\in R$
It is seen that $(-5,-6),(-6,-5)\in R$.

Also, $(-5,-5)\in R$.
$\therefore$ the relation $R$ is transitive.
Hence, relation $R$ is symmetric and transitive but not reflexive.