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 = ab

Question

Philoid · Accepted Answer

It is given that on Z⁺, define ∗ by a ∗ b = ab

We can see that for each a, b ϵ Z⁺, there is a unique element ab in Z⁺.

⇒ * carries each pair (a, b) to a unique element a * b = ab in Z⁺.

Therefore, * is a binary operation.

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 = ab