Translate the following inference to logic notation: For all x, if x_6 works, then x_6 is playing a game. There is at least one x for which x_6 will play a game if and only if x_6 will work. Therefore there is at least one x for which if x_6 works, then x_6 is playing a game.
forall x: P(x) -> Q(x). exists x: Q(x) <-> P(x). Therefore exists x: P(x) -> Q(x).