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