Translate the following inference to logic notation: For all x, if z were rich, then z is a taxi driver. For all x, if z drives a car, then z is rich. There is at least one x for which if z drives a car, then z is rich. For all x, if z were a taxi driver, then z is driving a car. Therefore there is at least one x for which z is rich if and only if z will drive a car.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: P(x) <-> R(x).