A logic network has two data inputs $A$ and $B$, and two control inputs $C_0$ and $C_1$. It implements the function $F$ according to the following table.
$${\begin{array}{|cc|c|}\hline
\textbf{$C_1$}& \textbf{$C_0$}& \textbf{F}\\\hline
0&0&\text{$\overline{A + B}$} \\ 0&1& \text{A + B} \\ 1&0& \text{$A \oplus B$ } \\ \hline
\end{array}}$$Implement the circuit using one $4$ to $1$ Multiplexer, one $2-$input Exclusive OR gate, one $2-$input AND gate, one $2-$input OR gate and one Inverter.