Translate the following inference to logic notation: For all x, if x were excited, then x is a police officer. For all x, if x were a nurse, then x is excited. There is at least one x for which if x were a police officer, then x is a nurse. Therefore there is at least one x for which x is excited if and only if x is a nurse.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> R(x). Therefore exists x: P(x) <-> R(x).