Show that the relation `R` defined by `R={(a , b):a-b` is divisible by `3; a , bZ}` is an equivalence relation.

Explanation

We observe the following relations of relation `R`.


Reflexivity:


Let a be an arbitrary element of `R_{.}`. Then,


`a-a=0=0 times 3`


`Rightarrow a-a` is divisible by `3`


`Rightarrow(a, a) in R` for all `a in Z`


So, `R` is reflexive on `Z`.


Symmetry:


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