Translate the following inference to logic notation: There is at least one x for which if z were sad, then z is a writer. For all x, z is sad. For all x, z is a nurse. For all x, if z were a writer, then z is an astronaut. Therefore there is at least one x for which z is an astronaut.
exists x: P(x) -> Q(x). forall x: P(x). forall x: R(x). forall x: Q(x) -> S(x). Therefore exists x: S(x).