Statement to predicate formula

Question

Let B(x) mean “x is a bird”,

let W(x) mean “x is a worm”,

let E(x, y) mean “x eats y”.

There is a statement "Only birds eat worms".

If we translate this statement to predicate formula it will become: $∀x∀y(W(x) ∧ E(y, x) → B(y))$

I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?

Answer 1

If we translate this statement to predicate formula it will become: $∀x∀y(W(x) ∧ E(y, x) → B(y))$

Anything will be a bird if it eats anything which is a worm.

Any eater of worms is a bird.

Only birds eat worms.

I was wondering will it be the same as $∀x∀y(B(x) ∧ E(x, y) → W(y))$ ?

Anything will be a worm if it is eaten by anything which is a bird.

Only worms are eaten by birds.