How would I convert this discrete math statement from logic/equation to English?

Question

Given that

• $B(x)$ means "$x$ is a bear",

• $F(x)$ means "$x$ is a fish", and

• $E(x,y)$ means "$x$ eats $y$",

what is the best English translation of

$\forall x[F(x)\rightarrow \forall y(E(y,x)\rightarrow B(y))]$ ?

How can I do solve this? I got "Every fish is eaten by some bear", but that is not the answer. I'm not entirely sure how to go about this since I am fairly new to Discrete Math. Any help is greatly appreciated.

Answer 1

It translates as : "For every fish, it is true that for anything that eats that fish, it is a bear". So ... this means that every fish only gets eaten by bears, i.e. That there is not anything that is not a bear that eats fish.

In short ... and colloquial English: Fish only get eaten by bears.

Answer 2

$\forall x~(F(x)\to\forall y~(E(y,x)\to B(y))$

$\forall x~(x\text{ is a fish}\to\forall y~(y\text{ eats $x$}\to y\text{ is a bear}))$

"If any fish is eaten by anything, then that thing is a bear."

Which I'd simplify to "Only bears eat fish."