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Let R ={(a, b):a,b in Z and (a-b) is div...

Let R ={(a, b):a,b in Z and (a-b) is divisible by 5 }. Show that R is an equivalence relation on Z.

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Here, `R = {(a,b):a,b in Z and (a-b)` is divisible by `5}`
For all `a in R`,
`=> (a-a) =0` and `0` is divisible by `5`.
`:. R` is reflexive.
Since in `R` for every `(a,b) in R`
`=> (a-b)` is divisible by `5`.
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