Consider a binary operation ∗ on N defined as a ∗ b = a3 + b3. Choose the correct answer.
On N, the operation * is defined as a * b = a3 + b3
For, a, b ϵ N, we get,
a * b = a3 + b3 = b3 + a3 = b * a [Addition is commutative in N]
⇒ the operation * is commutative.
We can observed that (1*2)*3 = (13+23)*3 = 9 * 3 = 93 + 33 = 729 + 27 = 756
Also, 1*(2*3) = 1*(23 +33) = 1*(8 +27) = 1 × 35 = 13 +353 = 1 + (35)3 = 1 + 42875 = 42876.
Therefore, (1 * 2)*3 ≠ 1*(2*3); where 1,2,3 ϵ N
Therefore, the operation * is not associative.
Therefore, the operation * is commutative, but not associative.