Let R be a relation from Q to Q defined by R = {(a,b); a,b ∈ Q and a−b ∈ Z}. Show that (i) (a,a) ∈ R for all a ∈ Q (ii) (a,b) ∈ R implies that (b,a) ∈ R (iii) (a,b) ∈ R and (b,c) ∈ R implies that (a,c) ∈ R