Given the Boolean function 

F = xyz + x'y'z + xyz 

a. List the truth table of the function. 

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

c. Simplify the algebraic expression using Boolean algebra. 

d. List the truth table of the function from the simplified expression and show that it is the same as the truth table in part (a). 

e. Draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part (b).