Translate the following inference to logic notation: For all x, if y works, then y is playing a game. There is at least one x for which if y plays a game, then y is working. For all x, if y plays a game, then y is working. Therefore there is at least one x for which if y works, then y is playing a game.
forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) -> Q(x).