$(30$ Points$)$

F $($A$,$ B$,$ C$,$ D$)=\backslash$Sigma $(1,2,4,7,10,11,12,13,15)$

Implement the Boolean Function mentioned above by

a$)$ using a $8$x$1$ multiplexer and external logic gates $(15$ points$)$

b$)$ using a $4$x$1$ multiplexer and external logic gates $(15$ points$).$