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 R, define * by a * b = a + 4b²

Here, Z⁺ denotes the set of all non-negative integers.

Answer 1

\[ a, b \in R\] 
\[ \Rightarrow a, 4 b^2 \in R\] 
\[ \Rightarrow a + 4 b^2 \in R\] 
\[ \Rightarrow a * b \in R\] 
\[\text{Therefore},\] 
\[a * b \in R, \forall a, b \in R\] 
\[\text{Thus}, * \text{ is a binary operation on R }.\]