Translate the following inference to logic notation: For all x, x_5 will write a letter or x_5 will not listen to a song. For all x, x_5 will not play a game. For all x, if x_5 writes a letter, then x_5 is playing a game. Therefore for all x, x_5 will not listen to a song.
forall x: P(x) or ~Q(x). forall x: ~R(x). forall x: P(x) -> R(x). Therefore forall x: ~Q(x).