Translate the following inference to logic notation: For all x, if y listens to a song, then y is drinking water. For all x, y is not a nurse. For all x, if y drinks water, then y is working. For all x, y is a nurse if and only if y will work. Therefore for all x, y will not listen to a song.
forall x: P(x) -> Q(x). forall x: ~R(x). forall x: Q(x) -> S(x). forall x: R(x) <-> S(x). Therefore forall x: ~P(x).