Prove that relation is an equivalence relation

Question

I have relation:

$a, b$ from $N(a,b)\in R$ only if $a+b$ is odd.

How can I prove that relation is an equivalence relation? Please explain to me.

Answer 1

This is not an equivalence relation.

Note that this relation is not transitive.

For example, $(1,2) \in R$ and $(2,3) \in R$, but $(1,3) \notin R$.