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