Translate the following inference to logic notation: For all x, if z were a nurse, then z is playing a game. If Michael were rich, then William is a nurse. For all x, if z plays a game, then z is a nurse. David is sleeping. William is playing a game or Michael is rich. Therefore David is sleeping and William is a nurse.
forall x: P(x) -> Q(x). p -> P(a). forall x: Q(x) -> P(x). q. Q(a) or p. Therefore q and P(a).