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 police officer. For all x, x_5 is a writer if and only if x_5 will play a game. For all x, if x_5 plays a game, then x_5 is a police officer. Therefore for all x, x_5 is not a writer.
forall x: P(x) -> Q(x). forall x: ~P(x). forall x: R(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore forall x: ~R(x).