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