Translate the following inference to logic notation: For all x, if x_3 were a soldier, then x_3 is driving a car. There is at least one x for which if x_3 were a scientist, then x_3 is a soldier. For all x, if x_3 drives a car, then x_3 is a scientist. Therefore there is at least one x for which if x_3 were a scientist, then x_3 is a soldier.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore exists x: R(x) -> P(x).