The question is, "What is the congruence class$[n]_5$ (that is, the equivalence class of $n$ with respect to congruence modulo 5) when n is
a) 2?
b)3?
c) 6?
d)−3?"
I know this is more work than the question is asking for, but I am just trying to get as much practice as I can with relations, and such. They didn't specify the set that I am going to find an equivalence class on, but I believe it is the integers, but am not certain why. But, if that is true, then I would have a relation, $R$, on the set $Z$, $R \subset Z$. And wouldn't we be able to determine the relation on this set, because a equivalence class is taken with respect to the relation? Would the relation be $R=\{(x,y)|x \equiv y~(mod~5)\}$? It just seems wrong for some reasons.