Translate the following inference to logic notation: For all x, if x_5 were rich, then x_5 is listening to a song. For all x, if x_5 listens to a song, then x_5 is rich. There is at least one x for which if x_5 were rich, then x_5 is curious. Therefore there is at least one x for which if x_5 listens to a song, then x_5 is curious.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: P(x) -> R(x). Therefore exists x: Q(x) -> R(x).