Translate the following inference to logic notation: There is at least one x for which x_9 is poor. For all x, x_9 is a lawyer if and only if x_9 is poor. For all x, if x_9 were a lawyer, then x_9 is cooking. For all x, x_9 will not cook. Therefore there is at least one x for which x_9 is a doctor.
exists x: P(x). forall x: Q(x) <-> P(x). forall x: Q(x) -> R(x). forall x: ~R(x). Therefore exists x: S(x).