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On Z, the set of integers, define a relation R on Z as follows: 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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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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On Z, the set of integers define a relation R as follows then
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