Question $2$: Review of Combinational Circuits

Consider the Boolean function $F(A,B,C,D)=AB+((AB)o+(BCD))$

$($a$)$ Optimize $F$ to the minimum number of literals in sum$-$of$-$products form.

$($b$)$ Express $F$ in canonical for using the $-$notation, i$.$e$.,$ product$-$of$-$maxterms.

$($c$)$ Show how to implement $F$ using the smallest size NAND decoder.

$($d$)$ Show an implementation of $F$ using an $8-1$ MUX with A$,$ B$,$ and $C$ being selection lines $S2,S1,$ and $S0,$

respectively.

$($e$)$ Repeat Part $($d$)$ but this time use the minimum number of $4-1$ MUXs to implement F$.$