Translate the following inference to logic notation: For all x, if x_1 drives a car, then x_1 is a soldier. For all x, if x_1 were a soldier, then x_1 is a taxi driver. There is at least one x for which if x_1 were a taxi driver, then x_1 is driving a car. Therefore there is at least one x for which x_1 is a taxi driver if and only if x_1 will drive a car.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: R(x) -> P(x). Therefore exists x: R(x) <-> P(x).