Given the following Boolean function:

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

$($a$)$ Obtain the truth table of the function

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

$($c$)$ Obtain the truth table of the function from the simplified expression and show that it is the same as

the one in part $($a$)$

$($d$)$ Draw the logic diagram from the simplified expression and compare the total number of gates with

the diagram of part $($b$)$