Translate the following inference to logic notation: For all x, if z were an astronaut, then z is a soldier. For all x, if z were a soldier, then z is an astronaut. For all x, z is an astronaut if and only if z is fast. For all x, z is not fast. Therefore for all x, z is not a soldier.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) <-> R(x). forall x: ~R(x). Therefore forall x: ~Q(x).