How do I translate "Alma does not eat anything unless she eats an apple" into predicate logic?

Question

Dictionary:

A: _ is apple, G: _ is green, D: _ eats _, a: Alma

What I came up with:

( ∃x(Ax ∧ Dax) → ∀xDax )

If there is an apple that Alma eats, then she eats anything.

I know it's not correct, but I don't know why...

Answer 1

A simpler way to write the sentence is "If Alma eats anything, she eats an apple". You need something in your dictionary for Alma eats ___.

Answer 2

∃x(Dax) → ∃y(Day ∧ Ay)

"If alma has eaten at least one thing, then she has eaten an apple."

Answer 3

I would say it is a somewhatcomplicated way of saying that she eats only apples. Thus it would be:

$\forall x \: (Dax \rightarrow Ax)$

Also, given your predicate $G$, was your sentence maybe meant to mean that she only eats green apples? In that case, it would be:

$\forall x \: (Dax \rightarrow (Ax \wedge Gx))$

Edit

No, I did read this incorrectly. It should be 'as long as she doesn't eat an apple, she doesn't eat anything at all'. So:

$\neg \exists x (Dax \wedge Ax) \rightarrow \neg \exists x \: Dax$

... Which is just the contrapositive of Dion's answer! Ok, this must be right.