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.

Question

Philoid · Accepted Answer

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

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

⇒ * carries each pair (a, b) to a unique element a * b = |a – b| 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 = |a – b|

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|