Translate the following inference to logic notation: There is at least one x for which if x_7 were a politician, then x_7 is a poet. For all x, x_7 is a politician or x_7 is not an astronaut. For all x, if x_7 were a poet, then x_7 is a police officer. Therefore there is at least one x for which if x_7 were an astronaut, then x_7 is a police officer.
exists x: P(x) -> Q(x). forall x: P(x) or ~R(x). forall x: Q(x) -> S(x). Therefore exists x: R(x) -> S(x).