Let `Z` be the set of all integers and `R` be the relation on `Z` defined as `R={(a, b); a,\ b\ in Z,` and `(a-b)` is divisible by `5}`. Prove that `R` is an equivalence relation.

Explanation

Here, `R = {(a,b):a,b in R and (a-b)` is divisible by `5}`

For all `a in R`,

`=> (a-a) =0` and `0` is divisible by `5`.

`:. R` is refexive.



Since in `R` for every `(a,b) in R`

`=> (a-b)` is divisible by `5`.

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