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