Exercise of equivalence relations

[Jerson]

how to solve this?

Be A = {1,2,3,4,5,6,7} and a relation R in the set A defined by:
xRy if “x − y is multiple of 3"

Prove that R is of equivalence and calculate the equivalence classes originated by R.

 

[pka]

how to solve this?
Be A = {1,2,3,4,5,6,7} and a relation R in the set A defined by:
xRy if “x − y is multiple of 3"
Prove that R is of equivalence and calculate the equivalence classes originated by R.

1) Is (x-x) divisible by three.
2) If (x-y) dividable by three then is (y-x) dividable by three ?
3) if (x-y) dividable by three and (y-z) dividable by three is it true that (x-z) dividable by three?