Translate the following inference to logic notation: For all x, z will listen to a song if and only if z will drink water. For all x, z will drink water if and only if z will listen to a song. Therefore for all x, if z drinks water, then z is listening to a song.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore forall x: Q(x) -> P(x).