Translate the following inference to logic notation: For all x, if z plays a game, then z is running. For all x, if z plays a game, then z is a nurse. For all x, if z were a nurse, then z is playing a game. For all x, z will not go running. For all x, if z goes running, then z is playing a game. Therefore for all x, z is not a nurse.
forall x: P(x) -> Q(x). forall x: P(x) -> R(x). forall x: R(x) -> P(x). forall x: ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: ~R(x).