Exercise $4(6$ points$)$ The function $f(a,b,c,d),$ is equal to $0$ if:

$a(b$ xor $c)=1,$ or

$a+b+d=0$

Write down the truth table for $f$

Write down the minimal SOP and POS forms for $f$

Implement f using a MUX with $4$ inputs

Write down $f$ in ALL$-$NAND form