Translate the following inference to logic notation: For all x, if x_5 were a police officer, then x_5 is playing a game. For all x, x_5 is not a writer. There is at least one x for which x_5 is a police officer or x_5 is a cashier. For all x, if x_5 plays a game, then x_5 is a writer. Therefore there is at least one x for which x_5 is a cashier.
forall x: P(x) -> Q(x). forall x: ~R(x). exists x: P(x) or S(x). forall x: Q(x) -> R(x). Therefore exists x: S(x).