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.

Answer 1

\[a, b \in Z^+ \] 
\[ \Rightarrow ab \in Z^+ \] 
\[ \Rightarrow a * b \in Z^+ \] 
\[\text{Therefore},\] 
\[a * b \in Z^+ , \forall a, b \in Z^+ \] 
\[\text{Thus}, * \text{ is a binary operation on } Z^+ .\]