The question is, "Give a description of each of the congruence classes modulo 6."
Well, I began saying that we have a relation, $R$, on the set $Z$, or, $R \subset Z \times Z$, where $x,y \in Z$. The relation would then be $R=\{(x,y)|x \equiv y~(mod~6)\}$
Then, $[n]_6 =\{x \in Z|~x \equiv n~(mod~6)\}$
$[n]_6=\{x \in Z|~6|(x-n)\}$
$[n]_6=\{x \in Z|~k(x-n)=6\}$, where $n \in Z$
As I looked over what I did, I started think that this would not describe all of the congruence classes on modulo 6. Also, what would I say k is? After despairing, I looked at the answer key, and they talked about there only being 6 equivalence classes. Why are there only six of them? It also says that you can describe equivalence classes as one set, how would I do that?