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