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