Q19 of 123 Page 3

Mark the correct alternative in each of the following:

On Z an operation * is defined by a * b = a2 + b2 for all a, b ∈ Z. The operation * on Z is


1) Commutative:


⇒ a * b = a2 + b2 …(1)


⇒ b * a = b2 + a2 …(2)


⇒ a * b= b * a


2) NOT Associative:


⇒ (a * b)* c = (a2 + b2) * c


= (a2 + b2)2 + c2


⇒ a * (b * c) = a * (b2 + a2)


= a2 + (b2 + c2)2


⇒ (a * b)* c ≠ a * (b * c)

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