$(50$ Points$)$ Use Boolean Identities to simplify the following Boolean functions. Show detailed

steps to earn full credits and list Boolean identities applied for each step.

a$)$

$f(A,B,C,D)\frac{?}{b}=ar((A+(\frac{?}{\text{b}\text{a}\text{r}}(C))+D)((\frac{?}{\text{b}\text{a}\text{r}}(B))+C)(A+(\frac{?}{\text{b}\text{a}\text{r}}(B))+D)((\frac{?}{\text{b}\text{a}\text{r}}(B))+C)((\frac{?}{\text{b}\text{a}\text{r}}(B))+C+(\frac{?}{\text{b}\text{a}\text{r}}(D))))$

b$)f(A,B,C,D)\frac{?}{b}=ar(A(\frac{?}{\text{b}\text{a}\text{r}}(B))C+AB\frac{+}{b}ar(ABC)+A(\frac{?}{\text{b}\text{a}\text{r}}(C))+AB(\frac{?}{\text{b}\text{a}\text{r}}(C)))$