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