Translate the following inference to logic notation: For all x, x_6 will listen to a song or x_6 will not play a game. For all x, if x_6 makes tea, then x_6 is playing a game. For all x, if x_6 listens to a song, then x_6 is making tea. Therefore for all x, x_6 will listen to a song if and only if x_6 will play a game.
forall x: P(x) or ~Q(x). forall x: R(x) -> Q(x). forall x: P(x) -> R(x). Therefore forall x: P(x) <-> Q(x).