Implement the Boolean function

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

$($a$)$ With AND, OR$,$ and NOT gates

$($b$)$ With OR$,$ and NOT gates

$($c$)$ With AND, and NOT gates

$($d$)$ With NAND, and NOT gates

$($e$)$ With NOR, and NOT gates