Translate the following inference to logic notation: For all x, if x_10 were an astronaut, then x_10 is running. There is at least one x for which if x_10 goes running, then x_10 is a cashier. For all x, x_10 is fast if and only if x_10 is an astronaut. For all x, if x_10 were a politician, then x_10 is fast. Therefore there is at least one x for which if x_10 were a politician, then x_10 is a cashier.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: S(x) <-> P(x). forall x: T(x) -> S(x). Therefore exists x: T(x) -> R(x).