Question

"Decide whether the following relations on Z is an equivalence relation or not. If it is, describe the partition (i.e. the equivalence classes) of Z created by the relation."

- What does it mean by "describe the partition..."?
For example, let a, b be integers (in Z): a is equivalent to b if (a+b) is
divisble by 2.
For that example, I was able to prove it to be an equivalence relation, I
just don't know how to "describe the partition of Z created by the relation".

Answer 1

there are two equivalence classes: even and odd
odd ~ odd because odd+odd is divisible by 2
even ~ even because even+even is divisible by 2
no even ~ odd, since even+odd is not divisible by 2.