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