Translate the following inference to logic notation: For all x, if z_3 plays tennis, then z_3 is driving a car. For all x, if z_3 were a janitor, then z_3 is playing a game. For all x, if z_3 drives a car, then z_3 is a janitor. There is at least one x for which z_3 will play tennis. Therefore there is at least one x for which z_3 will play a game.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). exists x: P(x). Therefore exists x: S(x).