I've been trying to learn formal logic but am somewhat confused. Given the following key, how would I symbolize the sentence "Everyone who trusts Ingmar trusts a vegetarian?"
Vx: x is a vegetarian.
Txy: x trusts y
In the text I'm using the correct answer is shown as ∀x[Txi→∃y(Txy&Vy)], but I was wondering what would be the effect of changing the scope of ∃y so that the sentence is instead symbolized as ∀x∃y[Txi→(Txy&Vy)]? Is there a difference between these two translations? From what I can tell, the first translation means that it's true for all x members of the domain that if x trusts Ingmar, then there is some y person such that x trusts y and y is a vegetarian. Whereas, if i'm interpreting this correctly, the second translation seems to say that it's true for all x people that there is some y person such that if x trusts Ingmar, then x also trusts y who is a vegetarian.