Q15 of 123 Page 3

Mark the correct alternative in each of the following:

Let * be a binary operation on R defined by a * b = ab + 1. Then, * is


1) Commutative:


⇒ a * b = ab + 1 …(1)


⇒ b * a = ba + 1 …(2)


⇒ a * b= b * a


2) NOT Associative:


⇒ (a * b)* c = (ab + 1) * c


(ab + 1) * c = (ab + 1)c + 1


(ab + 1) * c = abc + c + 1


⇒ a * (b * c) = a * (bc + 1)


a * (bc + 1) = a(bc + 1) + 1


a * (bc + 1) = abc + a


⇒ (a * b)* c ≠ a * (b * c)

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