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Question

Show that the relation R in the set R of real numbers defined as R={(a,b):ab2}  is neither reflexive nor symmetric nor transitive.


Solution

aa2 is not trueR is not reflexiveIf a = 2, b = 9ab2 but b > a2(a,b) ϵR but (b,a)RR is not symmetrica = 4, b = – 3, c = 1a b2 and b  c2 but a>c2R is not transitive

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