Translate the following inference to logic notation: For all x, if x_3 plays a game, then x_3 is driving a car. For all x, x_3 will play a game or x_3 will not drive a car. For all x, if x_3 drives a car, then x_3 is playing a game. Therefore for all x, x_3 will play a game if and only if x_3 will drive a car.
forall x: P(x) -> Q(x). forall x: P(x) or ~Q(x). forall x: Q(x) -> P(x). Therefore forall x: P(x) <-> Q(x).