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Let Z be the set of all integers and R b...

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.

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Thus, R being reflexive, symmetric and transitive, is an equivalence relation on Z.
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