Translate the following inference to logic notation: For all x, if y_1 plays a game, then y_1 is an office clerk. John is not an office clerk. For all x, y_1 is an office clerk if and only if y_1 will play a game. Therefore John is not playing a game.
forall x: P(x) -> Q(x). ~Q(a). forall x: Q(x) <-> P(x). Therefore ~P(a).