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