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 R, define ∗ by a ∗ b = ab²

Question

Philoid · Accepted Answer

It is given that On R, define ∗ by a ∗ b = ab²

We can see that for each a, b ϵ R, there is a unique element ab² in R.

⇒ * carries each pair (a, b) to a unique element a * b = ab² in R.

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 R, define ∗ by a ∗ b = ab2