Translate the following inference to logic notation: For all x, if z_1 were a writer, then z_1 is an astronaut. For all x, if z_1 were an astronaut, then z_1 is a writer. Therefore for all x, z_1 is a writer if and only if z_1 is an astronaut.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).