Using Boolean Algebra, simplify the following Boolean expressions to a minimum

number of literals:

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

$($b$)xz+x{y}^{\text{'}}+xyz+x^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}$

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

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