Given the following: $A{B}^{\text{'}}+C(A^{\text{'}}+B^{\text{'}})$

a$.(5$ points$)$ Draw a circuit which implements this using AND, OR$,$ and NOT gates. Do not simplify in any way first.

b$.(5$ points$)$ Now construct a truth table.

c$.(5$ points$)$ Use the sum of products to find an expression which results in the truth table and simplify it$.$

d$.(5$ points$)$ Create a circuit for the expression in c using AND, OR$,$ and NOT gates.

e$.(5$ points$)$ How many gates were required in part a compared to part d$?$