The question is, "Let R be the relation on the set of ordered pairs of positive integers such that $((a, b), (c, d)) ∈ R$ and only if $a+d=b+c$. Show that R is an equivalence relation."
There are two ways to prove this, but I only understand the second one.
The first way to proof: "By algebra, the given conditions is the same as the condition that $f((a,b))=f((c,d))$, where $f((x,y))=x-y$. Therefore, this is an equivalence relation."
I am not remotely sure of what they are doing...