I'm studying for my final exam of discrete mathematics, is an exercise in particular concerning equivalence relations do not know how to start:
$ \text{Let } A = \left\{{3, 5, 6, 8, 9, 11, 13}\right\}\text{ and } R \subseteq A\times A: xRy\Longleftrightarrow{ x \equiv y}$
How I can prove the symmetry, reflexivity and transitivity?
$(1)$ symmetry ($xRx$ for any $x$),
$(2)$ reflexivity ($xRy$ implies $yRx$), and
$(3)$ transitivity ($xRy$ and $yRz$ implies $xRz$)
I know clearly that the properties must be satisfied by other exercises I've done, but this one in specific, I do not know how to prove mathematically