Check the commutativity and associativity of each of the following binary operations:

‘o’ on Q defined by a o b = ab/2 for all a,b Q.

Given that ο is a binary operation on Q defined by for all a,bQ.


We know that commutative property is pοq = qοp, where ο is a binary operation.


Let’s check the commutativity of given binary operation:




b*a = a*b


The commutative property holds for given binary operation ο on Q.


We know that associative property is (pοq)οr = pο(qοr)


Let’s check the associativity of given binary operation:




...... (1)




...... (2)


From (1) and (2) we can clearly say that associativity hold for the binary operation ‘ο’ on ‘Q’.


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