Simplify each of the following Boolean equations. Sketch a reasonably simple combinational circuit implementing the simplified equation.

$($a$)Y\frac{?}{b}=ar(A)BC\frac{+}{b}ar(B(\frac{?}{\text{b}\text{a}\text{r}}(C)))+BC$

$($b$)Y=(\frac{?}{\text{b}\text{a}\text{r}}(A+B+C))D+AD+B.$

$($c$)Y=$ABCD$\frac{+}{b}ar(A)\frac{B}{b}ar(C)D\frac{+}{b}ar(((\frac{?}{\text{b}\text{a}\text{r}}(B))+D))E$