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On Z, the set of integers, define a relation R on Z as follows: $\mathrm{aRb}\text{if}\mathrm{ab}\ge 0$ 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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On **Z**, the set of integers define a relation R as follows $\mathrm{a},\mathrm{b}\in \mathbf{Z},\phantom{\rule{1em}{0ex}}\mathrm{aRb}\phantom{\rule{1em}{0ex}}\text{if}3\mid (2\mathrm{a}+\mathrm{b})$ then

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