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 a * b = ab
Answer» a ∈ Z⁺ , b ∈ Z⁺ , a * b = a^b b * a = b^a a * b ≠ b * a, hence * is not commutative (a * b) * c = ab * c = (a^b) c = a^bc a* (b * c) = a * b^c = (a)^bc (a * b) * c ≠ a* (b * c) hence * is not associative.

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

Answer»

a ∈ Z⁺ , b ∈ Z⁺ , a * b = a^b

b * a = b^a

a * b ≠ b * a,

hence * is not commutative

(a * b) * c = ab * c = (a^b) c = a^bc

a* (b * c) = a * b^c = (a)^bc

(a * b) * c ≠ a* (b * c)

hence * is not associative.