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