Translate the following inference to logic notation: For all x, x_8 will go running or x_8 will play a game. For all x, if x_8 goes running, then x_8 is rich. For all x, if x_8 plays a game, then x_8 is a police officer. There is at least one x for which x_8 is a police officer or x_8 is not rich. Therefore there is at least one x for which x_8 is a police officer.
forall x: P(x) or Q(x). forall x: P(x) -> R(x). forall x: Q(x) -> S(x). exists x: S(x) or ~R(x). Therefore exists x: S(x).