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