Consider the algebraic expressions for functions $F(x,Y,Z)$ and $G(A,B,C).$

$F(x,Y,Z)=xYZ+Y^{\text{'}}Z+x^{\text{'}}{Y}^{\text{'}}$

$G(A,B,C)=(A+B^{\text{'}})(A+C)(A^{\text{'}}+B+C)$

a$)$ Simplify the algebraic expressions for functions $F$ and $G$ using K$-$maps: obtain the expressions for

$F$ and $G$ in the sum$-$of$-$products $($SOP$)$ form with the minimal number of literals.

b$)$ Obtain the product$-$of$-$sums $($POS$)$ forms for $F$ and $G$ with the minimal number of literals.

Hint: use K$-$maps or apply distributive law to expressions in SOP form, delete consensus term.