Question

If $A=[x:f(x)=0]andB=[x:g(x)=0],$ then $A\cap B$ will be

Answer 1

Finding the value of $A\cap B$:

Given $A=[x:f(x)=0]andB=[x:g(x)=0],$

$$\begin{gathered} A\cap B=\{x:x\in Aandx\in B\} \\ =[x:f(x)=0andg(x)=0] \\ =[{f\left(x\right)}^2+{g\left(x\right)}^2] \\ A\cap B=0 \end{gathered}$$

Hence, the value of $\mathit{A}\mathbf{\cap }\mathit{B}$ is $\mathbf{0}$.