Given the function F$($x$,$y$,$z$)=$ y$($x$$z $+$ xz$)+$ x$($yz $+$ yz$)$

a$)$ List the truth table for F$.$

b$)$ Draw the logic diagram using the original Boolean expression.

c$)$ Simplify the expression using the K$-$Map.

d$)$ List the truth table for your answer in part c$.$

e$)$ Draw the logic diagram for the simplified expression in part c$.$