Equivalence relations and their class I am trying to figure out how to prove that an equivalence relation of the relation x~y defined on Z <=> x-y is a multiple of 3.
My attempt was:
1) Reflexive: x = x => x ~ x
2) Symmetric: x ~ y => x - y => - y + x => y ~ x
3) Transitive: ... <--- how do I make use of the fact that x-y is a multiple of 3?
Thanks for help! 

You have not proven anything.
$x-x=0$ is a multiple of $3$, so it is reflexive.
If $x-y=3k$ for some integer $k$, then $y-x=-3k$ is a multiple of $3$, so it is symmetric.
If $x-y=3m$ for some integer $m$ and $y-z=3n$ for some integer $n$, then $x-z=3(m+n)$ is a multiple of $3$, so it is transitive.
