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