Simplify the following expression using Boolean Algebra.

$($a$)F1=$ABC$\frac{+}{b}ar(A)C$

$($b$)F2=PQR+\frac{P}{b}ar(Q)R\frac{+}{b}ar(P)$

$($c$)F3=(\frac{?}{\text{b}\text{a}\text{r}}(RST))(\frac{?}{\text{b}\text{a}\text{r}}(R+S+T))$

$($d$)F4\frac{?}{b}=ar\frac{A}{b}ar\frac{B}{b}ar(C)\frac{+}{b}ar(A)BC+$ABC$+\frac{A}{b}ar\frac{B}{b}ar(C)+A\frac{B}{b}ar(C)$

$($e$)F5=(y\frac{+}{b}ar(z))(\frac{?}{\text{b}\text{a}\text{r}}(y)+z)\frac{+}{b}ar(x+y+z)$

$($f$)F6=(\frac{?}{\text{b}\text{a}\text{r}}(C+D))\frac{+}{b}ar(A)\frac{C}{b}ar(D)+\frac{A}{b}ar\frac{B}{b}ar(C)\frac{+}{b}ar\frac{A}{b}ar(B)CD+A\frac{C}{b}ar(D)$