Determine whether or not each of the definition of ∗ given below gives a binary operation. In the event that ∗ is not a binary operation, give justification for this.

1. On Z+, define ∗ by a ∗ b = a – b
2. On Z+, define ∗ by a ∗ b = ab

(i) On Z+ = {1, 2,3 , 4, 5,… … .}

Let a = 1 and b = 2

Subsequently, a ∗ b = a – b = 1 – 2 = – 1 ∉ Z+

activity * is certifiably not a parallel procedure on Z+ .

(ii) On Z+, characterize ∗ by a ∗ b = abdominal muscle

On Z+ = {1, 2,3 , 4, 5,… … .}

Let a = 2 and b = 3

Along these lines, a ∗ b = a b = 2 * 3 = 6 ∈ Z+ activity * is a paired procedure on Z+