For questions $8.-11.$ below consider the function f $($Y$,$ Z$,$ W$,$ X$)$ of four variables represented by the

following K$-$map.

f$($Y$,$Z$,$W$,$X$)$:

$11$

$01$

$01$

$01$

$01$

$11$

$01$

$00$

Y

W

Z

X

$8.(5$ points$)$

Which one of the following products are minterms of this function $($circle all minterms$)?$

Y ZX$$W $,$

Y $$Z$$XW$,$

Y $$ZXW$,$

Y Z$$XW$,$

Y Z$$XW $$

$4$

$9.(5$ points$)$

List all Prime Implicants $($PI$)$ of this function.

$10.(5$ points$)$

Give all Essential Prime Implicants $($EPI$)$ of this function $($if any$).$

$11.(5$ points$)$

Give a minimal sum$-$of$-$products expression for this function.