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