Question $3[25]$

a$)$ Using Laws of Boolean Algebra, simplify the following expressions:

i$)F\frac{?}{b}=ar(AB+A(\frac{?}{\text{b}\text{a}\text{r}}(C)))\frac{+}{b}ar\frac{A}{b}ar(B)C$

ii$),F=AB\frac{+}{b}ar(AC)+A(\frac{?}{\text{b}\text{a}\text{r}}(B))C(AB+C{)}_{?}$

$[5]$

$4$

iii$)$ Draw a truth table for a two input $($A and B$)$ logic system whose output is $B$ only if A is zero; otherwise, F inverts B$.$ State what type of logic gate would be needed to implement such a system.

$[3]$