$($a$)$ Implement the Boolean function $F(A,B,C,D),$ which can be expressed as sum of minterms $0,1,5,6,7,9,12,14$ with an $81$ multiplexer.

$($b$)$ Simplify the following boolean formula:

$A^{\text{'}}B+A^{\text{'}}BC+$ABC$+AB{C}^{\text{'}}$