$(5$ points each$)$ Simplify the following Boolean expressions using Boolean algebra and DeMorgan's.

Note: $A^{\text{'}}$ is the complement of $A.$ In textbooks, it is often A with a bar on top.

a$.A+AB$

b$.A+A^{\text{'}}B$

c$.A{B}^{\text{'}}{C}^{\text{'}}+AB{C}^{\text{'}}$

d$.A(A+A^{\text{'}}B+BC)$

e$.AC+A{C}^{\text{'}}+A^{\text{'}}B+A^{\text{'}}{B}^{\text{'}}$

f$.(A^{\text{'}}B{)}^{\text{'}}+A$

g$.(A^{\text{'}}{B}^{\text{'}}{)}^{\text{'}}+(A^{\text{'}}+C{)}^{\text{'}}$

h$.(A^{\text{'}}+B+C{)}^{\text{'}}$