Translate the following inference to logic notation: There is at least one x for which if y_2 were rich, then y_2 is listening to a song. For all x, y_2 is an astronaut. For all x, if y_2 listens to a song, then y_2 is not an astronaut. For all x, if y_2 listens to a song, then y_2 is rich. For all x, if y_2 listens to a song, then y_2 is rich. Therefore there is at least one x for which y_2 is not rich.
exists x: P(x) -> Q(x). forall x: R(x). forall x: Q(x) -> ~R(x). forall x: Q(x) -> P(x). forall x: Q(x) -> P(x). Therefore exists x: ~P(x).