$[10]$ Using properties of Boolean algebra, simplify the following Boolean expressions so they could be built with the minimum number of gates. These examples may help you with simplifying the longer expressions. Remember that A and $B$ can be replaced with any Boolean expression.

a$.x1=A+AB$

b$.x2=A^{\text{'}}+AB$

c$.x3=A^{\text{'}}B+AB$

d$.,x4=AB+A^{\text{'}}B$

e$.x5=AB+A^{\text{'}}{B}^{\text{'}}$

f$.x6=AB+(AB{)}^{\text{'}}$

g$.x7=AB+1$

h$.x8=A(A+B)$

i$.,x9=A^{\text{'}}(A+B)$

j$.,x10=(A^{\text{'}}+B^{\text{'}}{)}^{\text{'}}$