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

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

$($c$)xyz+x^{\text{'}}y+xy{z}^{\text{'}}$

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

$($e$)(a+b+c^{\text{'}})(a^{\text{'}}{b}^{\text{'}}+c)$

$($f$)a^{\text{'}}bc+ab{c}^{\text{'}}+abc+a^{\text{'}}b{c}^{\text{'}}$

Draw logic diagrams of the circuits that implement the original and simplified expressions Of $($a$),($c$),$ and $($d$).$Please only draw the circuits for a$,$ c$,$ and d and ensure your answer is correct.