Translate the following inference to logic notation: There is at least one x for which z is a nurse if and only if z will drink water. For all x, z will listen to a song or z is not a nurse. Therefore there is at least one x for which if z drinks water, then z is listening to a song.
exists x: P(x) <-> Q(x). forall x: R(x) or ~P(x). Therefore exists x: Q(x) -> R(x).