$(10$ points$)$ Draw the logic diagram for the following Boolean expression. The diagram should correspond exactly to the equation $($do not simplify$).$ Assume that the complements of the inputs are available.

F$($A$,$ B$,$ C$)=$ A$($BC$+$ B$$C$)+$ C$($A$+$ B$)$

$(10$ points$)$ Simplify the Boolean expression in $($a$)$ using a Karnaugh Map, then draw the corresponding two$-$level logic diagram as a sum of products implementation. Assume that the complements of the inputs are available.