Please answe question $2\mathrm{.}7$ using $2\mathrm{.}42\mathrm{.}4$ Reduce the following Boolean expressions to the indicated number of literais:

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

to three literals

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

to three literals

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

to one literal

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

to four literals

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

to two literals

$2\mathrm{.}7$ Draw logic diagrams of the circuits that implement the original and simplified expressions in Problem $2\mathrm{.}4($c$),($d$),$ and $($e$).$