How do I translate 'no philosopher student admires any rotten lecturer' into quantificational logic formula? Let's assume that $Fx=x$ is a philosophy student, $Rx=x$ is a rotten lecturer, and $Mxy=x$ admires $y$. My translation of the sentence was $\forall x(Fx\supset\neg\forall y(Ry\supset Mxy))$, but my logic textbook translated it as $\neg\exists x(Fx\wedge\exists y(Ry\wedge Mxy))$. As far as I know, `no philosophy student admires any rotten lecturer` means the same as `every philosophy student doesn't admire every rotten lecturer`. But, the textbook's author seems to understand it as `every philosophy student doesn't admire some rotten lecturer`. How do I wrap my mind around this?

The trip-up is that the usage of "any" _when inside a negated clause_ refers to "some" rather than "every".

Hence "No F admires any R" translates as "there does not exists an F that admires an R."

$$\
eg\exists x~\Big(F(x) \wedge \exists y~\big(R(y)\wedge M(x,y)\big)\Big)$$

Which is equivalent to $$\forall x~\Big(F(x)\to ~\forall y~\big(R(y)\big)\to \
eg M(x,y)\big)\Big)$$

Or in PNF: $$\forall x~\forall y~\Big(\big(F(x)\wedge R(y)\big) \to \
eg M(x,y)\Big)$$