Translate the following inference to logic notation: For all x, if x_9 listens to a song, then x_9 is a lawyer. There is at least one x for which if x_9 listens to a song, then x_9 is poor. For all x, x_9 will listen to a song if and only if x_9 is a lawyer. Therefore there is at least one x for which if x_9 were a lawyer, then x_9 is poor.
forall x: P(x) -> Q(x). exists x: P(x) -> R(x). forall x: P(x) <-> Q(x). Therefore exists x: Q(x) -> R(x).