A$.4$

Simplify the following Boolean equations using Boolean theorems. Check for correctness using a truth

table or K$-$map.

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

$($b$)Y=AB\frac{+}{b}ar(B)C\frac{+}{b}ar(AC)+BD+\frac{B}{b}ar(C)$

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