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