For each binary * operation defined below,determine * whether is commu

1.	For each binary * operation defined below,determine * whether is commutative or associative.On Z+ , define ab = 2“
Answer» a = Z⁺ , be Z⁺, ab = 2^ab b a = 2^ba = 2^ab a * b = b * a hence * is commutative (a * b) * c = 2^ab * c = 2^ab * c = 2^2al ’ ^x ‘ a(bc) = a* 2^ac= 2^a–2“ hence (a * b) * c * a * (b * c) ∴ * is not Associative.

For each binary * operation defined below,determine * whether is commutative or associative.On Z+ , define ab = 2“

Answer»

a = Z⁺ , be Z⁺,

a*b = 2^ab

b * a = 2^ba = 2^ab

a * b = b * a

hence * is commutative

(a * b) * c = 2^ab * c = 2^ab * c = 2^2al ’ ^x ‘

a*(b*c) = a* 2^ac= 2^a–2“

hence (a * b) * c * a * (b * c)

∴ * is not Associative.