Translate the following inference to logic notation: For all x, if z were a police officer, then z is a nurse. For all x, z is a police officer or z is not a nurse. Therefore for all x, z is a nurse if and only if z is a police officer.
forall x: P(x) -> Q(x). forall x: P(x) or ~Q(x). Therefore forall x: Q(x) <-> P(x).