Question

For each binary operation * defined below, determine whether * is commutative or associative.

(i) On Z, define a * b = a − b
(ii) On Q, define a * b = ab + 1
(iii) On Q, define a * b =ab/2
(iv) On Z+, define a * b = 2^ab
(v) On Z+, define a * b = a^b
(vi) On R − {−1}, define a_*b=a/(b+1)

Answer 1

Therefore, the operation * is not commutative. It can also be 

observed that

 Therefore, the operation * is not associative.