Q. 1 B4.3( 16 Votes )

# 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

Answer :

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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