Translate the following inference to logic notation: For all x, if x_1 were a doctor, then x_1 is climbing a mountain. For all x, x_1 is a doctor or x_1 will not climb a mountain. There is at least one x for which if x_1 were a doctor, then x_1 is climbing a mountain. Therefore there is at least one x for which if x_1 climbs a mountain, then x_1 is a doctor.
forall x: P(x) -> Q(x). forall x: P(x) or ~Q(x). exists x: P(x) -> Q(x). Therefore exists x: Q(x) -> P(x).