Question

a * b = `((a + b))/2` ∀a, b ∈ N is

पर्याय

• Associative

• Commutative

• Both associative and commutative

• Neither associative nor commutative

Answer 1

Commutative

Explanation:

a * b = `(a + b)/2 = (b + a)/2` = b * w show that `lambda` is commutative further. (a * b)* c = `((a + b)/2)`* c

= `(((a + b)/2) + c)/2`

= `(a + b + 2c)/4`

But a* (b*c) = a * `((b + c)/2)`

= `(a + (b + c)/2)/2`

= `(2a + b + c)/4 ≠ (a + b + 2c)/4` in general.

As a result, * is not associative.