Translate the following inference to logic notation: For all x, z is an astronaut if and only if z is a police officer. For all x, z is sad if and only if z is an astronaut. Therefore for all x, if z were sad, then z is a police officer.
forall x: P(x) <-> Q(x). forall x: R(x) <-> P(x). Therefore forall x: R(x) -> Q(x).