Multiplexer

$($a$)$ Implement the Boolean function with a $41$ multiplexer and external gates.

$F(A,B,C,D)=|$~$(3,8,12)$

$($b$)$ An $8-$to$-1$ multiplexer has inputs $A,B,$ and $C$ connected to the selection inputs $S2,S1,$ and $S0,$

respectively. The data inputs $10$ through $17$ are as follows:

$|1=12=17=0$;$13=15=1$;$10=14=D$; and $16=D^{\text{'}}$

Determine the Boolean function that the multiplexer implements.