I'm working on some discrete mathematics problems, and have run into an issue involving proving an equivalence relation.
The relation I'm tasked with proving is the relation $R$ defined on $\mathbb{Z}\times \mathbb{Z}$ by: $(a,b)R(c,d)\;\;\text{ if and only if}\;\;\; a+d = b+c.$
I understand the basic key components needed, like what's needed to prove reflexivity, symmetry, and transitivity, but I don't know how to plug the above information into these rules.
For instance, starting with proving reflexivity, I know that we must show that $(a,b)\in R$, but don't know how to do this with the constraints of $(a,b)R(c,d)$ if and only if $a+d = b+c$.