Exercise of equivalence relations

Jerson

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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.
 
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?
 
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