Translate the following inference to logic notation: For all x, y is excited or y will play a game. There is at least one x for which if y plays a game, then y is a server. For all x, if y were excited, then y is a server. Therefore there is at least one x for which y is a server.
forall x: P(x) or Q(x). exists x: Q(x) -> R(x). forall x: P(x) -> R(x). Therefore exists x: R(x).