Translate the following inference to logic notation: David is reading a book. For all x, if x_8 plays a game, then x_8 is sad. For all x, if x_8 were sad, then x_8 is playing a game. If Mary plays a game, then David is not reading a book. Therefore Mary is not sad.
p. forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). P(a) -> ~p. Therefore ~Q(a).