$4.$ Consider the algebraic expressions for functions F $($X$,$ Y$,$ Z$)$ and G $($A$,$ B$,$ C$).$

F $($X$,$ Y$,$ Z$)=$ XYZ $+$ Y$$Z $+$ X$$Y$$

G $($A$,$ B$,$ C$)=($A $+$ B$)($A $+$ C$)($A$+$ 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.