Translate the following inference to logic notation: There is at least one x for which if z were a politician, then z is a police officer. For all x, z will not work. For all x, z will work or z is not a police officer. For all x, if z listens to a song, then z is a politician. Therefore there is at least one x for which z will not listen to a song.
exists x: P(x) -> Q(x). forall x: ~R(x). forall x: R(x) or ~Q(x). forall x: S(x) -> P(x). Therefore exists x: ~S(x).