Given that * is a binary operation on N defined by a * b = \(\frac {a+b}{2}\) for all a,b∈N.
We know that commutative property is p*q = q*p, where * is a binary operation.
Let’s check the commutativity of given binary operation:
![](https://www.sarthaks.com/?qa=blob&qa_blobid=6925491745838919492)
∴ The commutative property holds for given binary operation ‘*’ on ‘N’.
We know that associative property is (p*q)*r = p*(q*r)
Let’s check the associativity of given binary operation:
![](https://www.sarthaks.com/?qa=blob&qa_blobid=14046874865680184261)
From (1) and (2) we can clearly say that associativity doesn’t hold for the binary operation ‘*’ on ‘N’.