Question -
Answer -
(a) Is * both associative and commutative?
(b) Is * commutative but not associative?
(c) Is * associative but not commutative?
(d) Is * neither commutative nor associative?
Solution
On N, the operation *is defined as a * b = a3 + b3.
For, a, b,∈ N, we have:
a * b = a3 + b3 = b3 + a3 = b * a [Addition is commutative in N]
Therefore,the operation * is commutative.
Itcan be observed that:
∴(1 * 2) * 3 ≠ 1 * (2 * 3) ; where 1, 2, 3 ∈ N
Therefore,the operation * is not associative.
Hence,the operation * is commutative, but not associative. Thus, the correct answeris B.