Translate the following inference to logic notation: For all x, if x_3 were a police officer, then x_3 is a doctor. There is at least one x for which if x_3 works, then x_3 is a police officer. For all x, x_3 will not work. For all x, if x_3 were a doctor, then x_3 is working. Therefore there is at least one x for which x_3 is not a police officer.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: ~R(x). forall x: Q(x) -> R(x). Therefore exists x: ~P(x).