Translate the following inference to logic notation: For all x, z will work or z will not play a game. For all x, z will work if and only if z will play a game. Therefore for all x, if z plays a game, then z is working.
forall x: P(x) or ~Q(x). forall x: P(x) <-> Q(x). Therefore forall x: Q(x) -> P(x).