Let `n` be a positive integer. Prove that the relation R on the set Z of all integers numbers defined by `(x , y) in R iff x-y` is divisible by `n ,` is an equivalence relation on Z.

Explanation

We have to check these properties on `R`.

Reflexivity:

Let `a in N`

Here, `a-a=0=0 times n`
`
Rightarrow a-a is divisible by n`
`

Rightarrow(a, a) in R `
`
Rightarrow(a, a) in R text { for all } a in Z`

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