Translate the following inference to logic notation: For all x, x_10 is excited. For all x, if x_10 were excited, then x_10 is an astronaut. For all x, x_10 will drink water. There is at least one x for which if x_10 were an astronaut, then x_10 is poor. Therefore there is at least one x for which x_10 is poor.
forall x: P(x). forall x: P(x) -> Q(x). forall x: R(x). exists x: Q(x) -> S(x). Therefore exists x: S(x).