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Question
Determine whether or not the definition of *given below gives a binary operation. In the event that * is not a binary operation give justification of this.
On Z+, defined * by a * b = ab
Here, Z+ denotes the set of all non-negative integers.
Solution
\[a, b \in Z^+ \]
\[ \Rightarrow ab \in Z^+ \]
\[ \Rightarrow a * b \in Z^+ \]
\[\text{Therefore},\]
\[a * b \in Z^+ , \forall a, b \in Z^+ \]
\[\text{Thus}, * \text{ is a binary operation on } Z^+ .\]
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