Translate the following inference to logic notation: For all x, if x_4 works, then x_4 is climbing a mountain. For all x, if x_4 climbs a mountain, then x_4 is a doctor. For all x, if x_4 were a doctor, then x_4 is working. Therefore if David were a doctor, then David is climbing a mountain.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore R(a) -> Q(a).