Translate the following inference to logic notation: For all x, x_7 will listen to a song or x_7 will not work. For all x, x_7 will work or x_7 will not listen to a song. There is at least one x for which x_7 will not work. Therefore there is at least one x for which x_7 will not listen to a song.
forall x: P(x) or ~Q(x). forall x: Q(x) or ~P(x). exists x: ~Q(x). Therefore exists x: ~P(x).