1.

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

Answer» Let R be a relation from Q to Q defined by R={(a,b): a,bQ and abZ}.

Show that:

(i) (a,a)R for all aQ

(ii) (a,b)R implies that (b,a)R

(iii) (a,b)R and (b,c)R implies that (a,c)R


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