Translate the following inference to logic notation: There is at least one x for which if z_1 were a soldier, then z_1 is driving a car. For all x, if z_1 were a soldier, then z_1 is driving a car. For all x, if z_1 drives a car, then z_1 is a taxi driver. For all x, if z_1 were a taxi driver, then z_1 is a soldier. Therefore there is at least one x for which z_1 will drive a car if and only if z_1 is a soldier.
exists x: P(x) -> Q(x). forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: Q(x) <-> P(x).