Regarding a counterexample to the reflexivity of a divisibility relation on $\Bbb Z$

Question

I'm asked to either prove or disprove if the relation on all integers $\Bbb Z$ is an equivalence relation for $x \sim y$ if and only if $x+y$ is divisible by $3$. From my understanding, the relation can't be reflexive as if $x=1$ then $x+x=2$ which is not divisible by $3$. Is giving counter examples a correct way to disprove an equivalence relation and is the given counter example appropriate for this question?

Answer 1

Yes, giving a counter-example as you have done is a correct way to disprove the assertion that this is an equivalence relation. Your counter-example is fine.