Q. 4 G5.0( 1 Vote )

Check the commuta

Answer :

Given that * is a binary operation on Q defined by a*b = a + ab 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 + ab


b*a = b + ba = b + ab


b*a≠a*b


Commutative property doesn’t 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 + ab)*c


(a*b)*c = a + ab + ((a + ab)×c)


(a*b)*c = a + ab + ac + abc ...... (1)


a*(b*c) = a*(b + bc)


a*(b*c) = a + (a×(b + bc))


a*(b*c) = a + ab + abc ...... (2)


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


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