Translate the following inference to logic notation: For all x, x_2 is a doctor or x_2 will climb a mountain. For all x, x_2 is not a doctor. For all x, if x_2 climbs a mountain, then x_2 is an astronaut. Therefore for all x, x_2 is an astronaut.
forall x: P(x) or Q(x). forall x: ~P(x). forall x: Q(x) -> R(x). Therefore forall x: R(x).