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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

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.

(ii) On Z^+ , define ∗ by a * b = ab

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(ii) On Z^+ , define ∗ by a * b = ab

 We can observe that for a,b \in Z^+,there is a unique element ab in Z^+.

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

Therefore,* is a binary operation.

 

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