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On Z, the set of integers, define a relation R on Z as follows: $aRb if ab \geq 0$ then

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a

R is reflexive

b

R is symmetric

c

R is not transitive

d

R is an equivalence relation

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detailed solution

Correct option is A

For each a∈Z,aRa as a2≥0R is reflexive. Next, if a R b, then ab≥0⇒ ba≥0⇒bRa⇒R is symmetric.Next, supposea=-1, b = 0, c = 8 Then a R b as ab ≥ 0 and b R c as bc ≥ 0 but a is not related to c as ac =-8 < 0. Thus, R is reflexive, symmetric but not transitive

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