Translate the following inference to logic notation: For all x, x_4 is poor or x_4 is not rich. There is at least one x for which x_4 is rich if and only if x_4 is poor. Therefore there is at least one x for which x_4 is rich if and only if x_4 is poor.
forall x: P(x) or ~Q(x). exists x: Q(x) <-> P(x). Therefore exists x: Q(x) <-> P(x).