Translate the following inference to logic notation: For all x, x_11 is happy or x_11 will work. There is at least one x for which if x_11 listens to a song, then x_11 is working. For all x, if x_11 works, then x_11 is listening to a song. For all x, x_11 is not happy. Therefore there is at least one x for which x_11 will listen to a song.
forall x: P(x) or Q(x). exists x: R(x) -> Q(x). forall x: Q(x) -> R(x). forall x: ~P(x). Therefore exists x: R(x).