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Let R be the relation of the set Z of al...

Let R be the relation of the set Z of all integers defined by :
`R = {(a,b) : a, b in Z and (a-b) " is divisible by " n in N}`
Prove that :
(i) `(a,a) in R` for all a `in Z`
(ii) `(a,b) in R rArr (b,a) in R` for all `a, b in Z`
(iii) `(a,b) in R and (b,c) in R rArr (a,c) in R " for all" a,b,c in Z`

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