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!