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