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