Translate the following inference to logic notation: For all x, x_12 is rich. For all x, if x_12 were rich, then x_12 is taking a plane. For all x, x_12 is a police officer. There is at least one x for which if x_12 takes a plane, then x_12 is a politician. Therefore there is at least one x for which x_12 is a politician.
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).