Translate the following inference to logic notation: For all x, if x_5 drives a car, then x_5 is working. For all x, if x_5 were an astronaut, then x_5 is driving a car. For all x, if x_5 takes a plane, then x_5 is an astronaut. There is at least one x for which x_5 will take a plane. Therefore there is at least one x for which x_5 will work.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) -> R(x). exists x: S(x). Therefore exists x: Q(x).