Translate the following inference to logic notation: There is at least one x for which x_10 will work. For all x, if x_10 works, then x_10 is running. For all x, if x_10 goes running, then x_10 is listening to a song. Therefore there is at least one x for which x_10 will listen to a song or x_10 is sad.
exists x: P(x). forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). Therefore exists x: R(x) or S(x).