Given the function $F(x,y,z)=y(x^{\text{'}}z+x{z}^{\text{'}})+x(yz+y{z}^{\text{'}})$

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$.$