Let $R$ be a subset of Z $*$ Z, the relation being congruent mod 4.
How many equivalence relations $E$ are such that $R$ is a subset of $E$ and $E$ is a subset of Z $*$ Z.
I know that (mod 4) has 4 equivalence classes. But I am stuck with this fact. Does this mean that $R$ is composed of these 4 equivalence classes? Wouldn't that mean that $E$ has an infinite amount of equivalence relations, composed by all the equivalence classes greater than 3?
I am just starting to see the concept of relations. So, it would be a lot of help if you could give me any tips on solving this problem!