Parts $($a$),($b$),$ and $($c$)$ refer to the following Boolean expression:

$F=AC+AB{C}^{\text{'}}+B^{\text{'}}C+BC$

a$.(10$ points$)$ Create a truth table for the expression.

b$.(10$ points$)$ Simplify the expression using a Karnaugh map.

c$.(10$ points$)$ Draw the two$-$level logic diagram for the simplified expression using only NAND gates and inverters. Assume that the complements of the inputs are not available.