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 = ab


It is given that on Z+, define by a b = ab

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


* carries each pair (a, b) to a unique element a * b = ab in Z+.


Therefore, * is a binary operation.


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