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.
On Z⁺, define ∗ by a ∗ b = a – b

Question

Philoid · Accepted Answer

It is given that On Z⁺, define ∗ by a ∗ b = a – b

It is not a binary operation as the image of (1, 2) under * is

1 * 2 = 1 – 2 = -1 Z⁺.

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.On Z+, define ∗ by a ∗ b = a – b