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Home  >>  AIMS  >>  Class11  >>  Math  >>  Relations and Functions
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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) $ \in $ R (iii) (a,b) $ \in $ R and (b,c) $ \in $ R implies that (a,c) $ \in $ R

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(i) Since, a – a = 0 $ \in $ Z, if follows that (a, a) $ \in $ R.
(ii) (a,b) $ \in $ R implies that a – b $ \in $ Z. So, b – a $ \in $ Z. Therefore, (b, a) $ \in $ R
(iii) (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
answered Jun 29, 2014 by thanvigandhi_1
 

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