Simplify the following Boolean expressions $(50$ points$)$

a$.\frac{\frac{?}{?}}{\frac{?}{?}}$bar $\frac{A}{b}ar\frac{B}{b}ar(C)\frac{+}{b}ar\frac{A}{b}ar(B)C\frac{+}{b}ar(A)\frac{B}{b}ar(C)+\frac{A}{b}ar\frac{B}{b}ar(C)$

b$.\frac{?}{\text{b}\text{a}\text{r}}(A)B+\frac{A}{b}ar(B)\frac{+}{b}ar((AB\frac{+}{b}ar(CD)))\frac{+}{b}ar(A)\frac{B}{b}ar(C)D$

c$.\frac{?}{\text{b}\text{a}\text{r}}((E+F)((\frac{?}{\text{b}\text{a}\text{r}}(G))+H))+\frac{E}{b}ar(F)G\frac{+}{b}ar(E)(F\frac{+}{b}ar(H))$

d$.\frac{?}{\text{b}\text{a}\text{r}}((A+(\frac{?}{\text{b}\text{a}\text{r}}(B)))(C+(\frac{?}{\text{b}\text{a}\text{r}}(D))))*(\frac{A}{b}ar(C)+BD)\frac{+}{b}ar(A)(B\frac{+}{b}ar(C))*(D\frac{+}{b}ar(B)C)$

e$.\frac{?}{\text{b}\text{a}\text{r}}((A(\frac{?}{\text{b}\text{a}\text{r}}(B))C+AB)+((A+B)(C+B)))$