$2\mathrm{.}7$ Draw logic diagrams of circuits that implement the original and simplified expressions in

Problem $2\mathrm{.}4($a$),($c$),$ and $($e$).$

$2\mathrm{.}4$ Reduce the following Boolean expressions to the indicated number of literals:

$($a$)*x^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}+y+x{y}^{\text{'}}{z}^{\text{'}}$

to two literals

$($b$)*x^{\text{'}}y(x^{\text{'}}+z^{\text{'}})+x^{\text{'}}y+xyz$

to three literals

$($c$)*(x+yz{)}^{\text{'}}+(x+y^{\text{'}}{z}^{\text{'}}{)}^{\text{'}}$

to one literal

$($d$)*(w^{\text{'}}+x)(w+y)(x^{\text{'}}+y)(w+xyz)$

to four literals

$($e$)wx{y}^{\text{'}}{z}^{\text{'}}+w{y}^{\text{'}}+w{x}^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}$

to two literals