Translate the following inference to logic notation: For all x, x_8 is rich if and only if x_8 is an astronaut. There is at least one x for which if x_8 were a cashier, then x_8 is working. For all x, if x_8 works, then x_8 is an astronaut. Therefore there is at least one x for which if x_8 were a cashier, then x_8 is rich.
forall x: P(x) <-> Q(x). exists x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore exists x: R(x) -> P(x).