Q$10.$ Simplify the following Boolean expressions to a minimum number of literals:

a$.xy+x{y}^{\text{'}}$

b$.(x+y)(x+y^{\text{'}})$

c$.xyz+x^{\text{'}}y+xy{z}^{\text{'}}$

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

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