$.$ For the Boolean function F $=$ xy$$z $+$ x$$y$$z $+$ w$$xy $+$ wx$$y $+$ wxy $($a$)$ Obtain the truth table of F$.($b$)$ Draw the logic diagram, using the original Boolean expression. $($c$)$ Use Boolean algebra to simplify the function to a minimum number of literals. $($d$)$ Draw the logic diagram from the simplified expression, and compare the total number of gates with the diagram of part $($b$).$