Translate the following inference to logic notation: For all x, if x_9 were a doctor, then x_9 is a nurse. There is at least one x for which if x_9 were excited, then x_9 is a doctor. For all x, x_9 is excited if and only if x_9 is a sailor. For all x, x_9 is not a nurse. Therefore there is at least one x for which x_9 is not a sailor.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: R(x) <-> S(x). forall x: ~Q(x). Therefore exists x: ~S(x).