Determine wherther or not each of the defintion of ∗ given below gives a binary operation. In the event that ∗ is not a binary operation, give justification for this.
(ii) ON Z+, defined ∗ by a∗b=ab
On Z+, ∗ is defined by a∗b=ab.
It is seen that for each a,b in Z+, there is a unique element ab in Z+.
This means that as ∗ carries each pair (a,b)to a unique element a∗b=ab in Z+.
Therefore, ∗ is a binary operation.