Q. 4 I5.0( 1 Vote )

Check the commuta

Answer :

Given that * is a binary operation on Q defined by a*b = (a – b)2 for all a,bQ.


We know that commutative property is p*q = q*p, where * is a binary operation.


Let’s check the commutativity of given binary operation:


a*b = (a – b)2


b*a = (b – a)2 = (a – b)2


b*a = a*b


Commutative property holds for given binary operation * on Q.


We know that associative property is (p*q)*r = p*(q*r)


Let’s check the associativity of given binary operation:


(a*b)*c = ((a – b)2)*c



(a*b)*c = (a2 + b2 – 2ab – c)2 ...... (1)


a*(b*c) = a*((b – c)2)



a*(b*c) = (a2 – b2 – c2 + 2bc)2 ...... (2)


From (1) and (2) we can clearly say that associativity doesn’t hold for the binary operation ‘*’ on ‘Q’.


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