Consider the function $F(A,B,C)={\displaystyle \underset{?}{\overset{?}{}}}(0,1,2,3,4,7).$ Assume $C$ is the LSB

a$)(\text{'}$ Vrite the truth table of $F.$

b$)$ Write the logic expression of $F$ in the Sum$-$of$-$Product $($SOP$)$ form.

c$)$ Synthesize the logic expression found in part $($b$)$ above using AND$/$OR$/$NOT gates.

d$)$ Transform the logic network found in part $($c$)$ above using only NAND gates. Note: You need to use the NAND gate to design the NOT functionality.

e$)$ Write a Verilog module that describes the expression of $F$ using the "assign" statement.