Translate the following inference to logic notation: For all x, if y plays a game, then y is not listening to a song. There is at least one x for which y is a bartender if and only if y will play a game. For all x, y will listen to a song. Therefore there is at least one x for which y is not a bartender.
forall x: P(x) -> ~Q(x). exists x: R(x) <-> P(x). forall x: Q(x). Therefore exists x: ~R(x).