English translation to First Order Logic

Question

I have to create a scenario using FOL and i am having confusions for this particular sentence.

Sentence: 9. If someone gets a seat in engineering, he will not get a seat in CS.

Which of the following FOL are correct to represent the above sentence?

∃x (get(x,EngSeat) --> ¬ get(x,CSseat))

∃x (get(x,EngSeat) ∧ ¬ get(x,CSseat))

Also, i replace 'someone' by 'anyone' in the above sentence, should i replace ∃x by ∀ x?

Answer 1

Neither is correct. The correct translation is:

$~~~~~~\forall x: [Student(x) \implies [Gets(x, EngSeat) \implies \neg Gets(x, CSSeat)]]$

Edit: Where $Student$ is a unary predicate, $Gets$ is a binary predicate, $x$ is a bound variable, and both $EngSeat$ and $CSSeat$ are free variables.

Edit: Equivalently and perhaps more natural:

$~~~~~~\forall x: [Student(x) \implies \neg [Gets(x, EngSeat) \land Gets(x, CSSeat)]]$