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