Translate the following inference to logic notation: For all x, if z plays a game, then z is cooking. For all x, if z cooks, then z is playing a game. Thomas is not playing a game. Therefore Thomas is not cooking or Joseph is an astronaut.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). ~P(a). Therefore ~Q(a) or p.