Translate the following inference to logic notation: For all x, z will not listen to a song. For all x, if z were rich, then z is driving a car. For all x, z is an astronaut if and only if z will drive a car. For all x, if z drives a car, then z is rich. For all x, z is a mechanic if and only if z will listen to a song. For all x, z is an astronaut if and only if z is a mechanic. Therefore for all x, z is not rich.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: S(x) <-> R(x). forall x: R(x) -> Q(x). forall x: T(x) <-> P(x). forall x: S(x) <-> T(x). Therefore forall x: ~Q(x).