Translate the following inference to logic notation: For all x, z will go running if and only if z is a nurse. For all x, if z were an astronaut, then z is a nurse. For all x, if z goes running, then z is an astronaut. Therefore for all x, if z were a nurse, then z is running.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). forall x: P(x) -> R(x). Therefore forall x: Q(x) -> P(x).