Question $5(5$ points$)-$ Implementing boolean function using PLA

Consider the following two Boolean functions given as follow:

$F_1(a,b,c)=(3,5,6,7)$

$F_2(a,b,c,d)=(0,1,2,3,4)$

Implement using a PLA the minimized Boolean expression of $F_1(1pt)$

Implement using a PLA the minimized Boolean expression of $F_2(1pt)$

Prouve that both functions $F_1$ and $F_2$ are composed of only three $(3)$ terms $(2pt)($hint:

compute the expression of $F_2^{\text{'}}.$ You can do it using $K-$maps$).$ Identify these terms.

By adding additional ORs and XORs, implement $F_1$ and $F_2$ in a PLA of $3$ ANDS $(1$ pt$)$