Translate the following inference to logic notation: For all x, if x_7 sleeps, then y_2 is listening to a song. For all x, x_7 will sleep or x_7 is happy. For all x, y_2 will listen to a song or x_7 is not happy. Therefore there is at least one x for which y_2 will listen to a song.
forall x: P(x) -> Q(x). forall x: P(x) or R(x). forall x: Q(x) or ~R(x). Therefore exists x: Q(x).