Translate the following inference to logic notation: There is at least one x for which if y were a scientist, then y is an artist. For all x, y will listen to a song if and only if y is an artist. For all x, if y were a bartender, then y is a scientist. 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) -> Q(x). forall x: R(x) <-> Q(x). forall x: S(x) -> P(x). Therefore exists x: S(x) -> R(x).