Q1 of 107 Page 24

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

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.


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