Translate the following inference to logic notation: There is at least one x for which if x_8 drinks water, then x_8 is an astronaut. For all x, x_8 will go running if and only if x_8 will drink water. For all x, if x_8 were an astronaut, then x_8 is driving a car. Therefore there is at least one x for which if x_8 goes running, then x_8 is driving a car.
exists x: P(x) -> Q(x). forall x: R(x) <-> P(x). forall x: Q(x) -> S(x). Therefore exists x: R(x) -> S(x).