Translate the following inference to logic notation: For all x, z is a doctor or z will listen to a song. For all x, z is a police officer if and only if z will listen to a song. There is at least one x for which z is an astronaut if and only if z is a sailor. For all x, z is not a doctor or z is a sailor. For all x, if z were an astronaut, then z is a police officer. Therefore there is at least one x for which z is a police officer.
forall x: P(x) or Q(x). forall x: R(x) <-> Q(x). exists x: S(x) <-> T(x). forall x: ~P(x) or T(x). forall x: S(x) -> R(x). Therefore exists x: R(x).