Inputs A and $B$ will be connected to the selection lines of the multiplexer. The input requirements for the data lines of the multiplexer will be functions of inputs $C$ and $D.$ This is achieved by expressing $F$ as a function of $C$ and $D$ for each of the four cases, $AB=00,AB=01,AB=10$ and $AB=11,$ which must be implemented using external logic gates.

a$.(5$ points$)$ Generate the truth table for $F.$

b$.(10$ points$)$ Formulate the expressions for the four data lines as functions of inputs $C$ and $D.$

c$.(10$ points$)$ Implement the logic circuit for $F$ using the $4-$to$-1$ line multiplexer and external logic gates. Do not just put the expressions next to the data lines. Use logic gates to implement the expressions for the four data lines. Use inverters if the complements of the inputs are needed.