Translate the following inference to logic notation: For all x, z_4 will not listen to a song. For all x, if z_4 listens to a song, then z_4 is a soldier. For all x, z_4 will listen to a song if and only if z_4 is a soldier. Therefore for all x, z_4 is not a soldier.
forall x: ~P(x). forall x: P(x) -> Q(x). forall x: P(x) <-> Q(x). Therefore forall x: ~Q(x).