Problem$\_$#$01]$ Using Boolean algebra techniques, simplify as much as possible.

$($a$)A(A+B)$

$($b$)A(\frac{?}{\text{b}\text{a}\text{r}}(A)+AB)$

$($c$)BC\frac{+}{b}ar(B)C$

$($d$)A(A\frac{+}{b}ar(A)B)$

$($e$)\frac{A}{b}ar(B)C\frac{+}{b}ar(A)BC\frac{+}{b}ar\frac{A}{b}ar(B)C$

Problem$\_$#$02]$ Using Boolean algebra techniques, simplify the expressions below.

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

$($b$)\frac{?}{\text{b}\text{a}\text{r}}(A)B\frac{+}{b}ar(A)\frac{B}{b}ar(C)\frac{+}{b}ar(A)BCD\frac{+}{b}ar(A)\frac{B}{b}ar\frac{C}{b}ar(D)E$

$($c$)AB\frac{+}{b}ar(AB)C+A$

$($d$)(A\frac{+}{b}ar(A))(AB+A\frac{B}{b}ar(C))$

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

Problem$\_$#$03]$ Determine which of the logic circuits below are equivalent.

$($a$)$

$($b$)$

$($c$)$