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