Translate the following inference to logic notation: For all x, x_9 will not play a game or x_9 is an astronaut. For all x, x_9 is fast or x_9 will play a game. For all x, x_9 is not fast. Barbara is not cooking. Therefore Barbara is an astronaut.
forall x: ~P(x) or Q(x). forall x: R(x) or P(x). forall x: ~R(x). ~S(a). Therefore Q(a).