Translate the following inference to logic notation: For all x, x is an astronaut or x is not a nurse. There is at least one x for which if x were a writer, then x is a nurse. For all x, if x were an astronaut, then x is a writer. Therefore there is at least one x for which if x were an astronaut, then x is a nurse.
forall x: P(x) or ~Q(x). exists x: R(x) -> Q(x). forall x: P(x) -> R(x). Therefore exists x: P(x) -> Q(x).