$2\mathrm{.}18$ For the Boolean function

$F=x{y}^{\text{'}}z+x^{\text{'}}{y}^{\text{'}}z+w^{\text{'}}xy+w{x}^{\text{'}}y+wxy$

$($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$)$ Obtain the truth table of the function from the simplified expression and show that

it is the same as the one 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$).$