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Let R be a relation from Q to Q defined ...

Let R be a relation from Q to Q defined by `R={(a,b): a,b in Q and a-b in Z}`. Show that
(i) `(a,a) in R" for all " a in Q`
(ii) `(a,b) in R` implies that `(b,a) inR `
(iii) `(a,b) in R and (b,c) in R` implies that `(a,c) in R`

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The correct Answer is:
(a,b) and `(b, c) in R` implies that `a-b in Z. b-c in Z`. So, a-c= (a-b) + (b-c) in Z`. Therefore `(a, c) in R`
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