Question

Determine which of the following binary operation on the Set N are associate and commutaive both.

Options

• a* b = 1 ∀ a, b ∈ N

• a* b = `((a + b))/2` ∀ a, b ∈ N

• a* b = 0 ∀, a, b ∈ R

• a* b = – 1, ∀ a, b ∈ N

Answer 1

a* b = 1 ∀ a, b ∈ N

Explanation:

Clearly by definition a*b = b*a = 1, ∀a, b ∈ N.

Also (a*b)*c = (1*c) = 1 and a*(b*c) = a*(1) = 1 a, b, c ∈ N.

As a result, 'R' is both associative and commutative.