Q.1 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.

(iii) On R, define ∗ by a * b = ab^2

Answers (1)

(iii) On R, define ∗ by a * b = ab^2

 We can observe that for a,b \in R,there is a unique element ab^{2}  in R.

This means * carries each pair (a,b)  to a unique element a * b = ab^{2} in R.

Therefore,* is a binary operation.

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