Translate the following inference to logic notation: For all x, x is a police officer or x will not work. There is at least one x for which if x were a police officer, then x is working. Therefore there is at least one x for which if x works, then x is a police officer.
forall x: P(x) or ~Q(x). exists x: P(x) -> Q(x). Therefore exists x: Q(x) -> P(x).