Translate the following inference to logic notation: For all x, x_9 will sleep or x_9 will not listen to a song. There is at least one x for which x_9 will listen to a song if and only if x_9 will work. Therefore there is at least one x for which if x_9 works, then x_9 is sleeping.
forall x: P(x) or ~Q(x). exists x: Q(x) <-> R(x). Therefore exists x: R(x) -> P(x).