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