Let ‘&’ be a binary operation defined on the set N. Which of the following definitions is commutative but not associative? ans. a & b=a+b a & b=a-b a & b=ab a & b=ab – 8

The operation that is commutative but not associative among the given options is a & b = a - b.

Let's break it down:

1. Commutative property: An operation is commutative if changing the order of the operands does not change the result. In the case of a & b = a - b, it is commutative because if you swap a and b, the result remains the same. For example, if a = 3 and b = 2, then a - b = 1 and b - a = -1, which are not the same. Therefore, this operation is not commutative.

2. Associative property: An operation is associative if the way in which the operands are grouped does not change the result. In the case of a & b = a - b, it is not associative because the grouping of operands can affect the result. For example, if a = 3, b = 2, and c = 1, then (a - b) - c = 0, but a - (b - c) = 2, which are not the same. Therefore, this operation is not associative.

So, the operation a & b = a - b is not commutative and not associative.

The other operations a & b = a + b and a & b = ab are both commutative and associative. The operation a & b = ab - 8 is not commutative.