Translate the following inference to logic notation: For all x, if x_15 were fast, then x_15 is a doctor. Jennifer is not a doctor. For all x, if x_20 plays a game, then x_20 is sleeping. Jennifer is fast if and only if Joseph is sleeping. Therefore Joseph is not playing a game.
forall x: P(x) -> Q(x). ~Q(a). forall x: R(x) -> S(x). P(a) <-> S(b). Therefore ~R(b).