Predicate logic translation

Question

Given:

$Sx: x$ is a sith

$Kxy: x$ kills $y$

$Dx: x$ succumbs to the dark side.

Translate: Not everyone who kills a Sith succumbs to the dark side.

Answer 1

Start with the English:

Not (everyone who kills a sith succumbs to the dark side)

Give the implicit people names:

Not (everyone, $a$, who kills a sith, $b$, succumbs to the dark side)

Not is a '$\neg$':

$\neg($ for everyone$, a,$ who (kills a sith $b$) implies $a$ succumbs to the dark side)

Saying (kills a sith $b$) can be translated as $\exists b(b$ is a sith and $a$ kills $b)$

$\neg($ for everyone, $a$, $\exists b(b$ is a sith and $a$ kills $b)$ implies $a$ succumbs to the dark side)

quantify over $a$ to account for 'everyone':

$\neg\forall a( \exists b(b$ is a sith and $a$ kills $ b)$ implies $a$ succumbs to the dark side)

finish:

$\neg\forall a(\exists b(Sb\wedge Kab)\rightarrow Da)$

Answer 2

$\sim (\forall x,y) ( Sy \wedge Kxy \wedge Dx )$

Replace "For all" with upside down A