Translate the following inference to logic notation: For all x, if y_2 were excited, then y_2 is an astronaut. For all x, if y_2 cooks, then y_2 is excited. For all x, y_2 will drive a car if and only if y_2 is an astronaut. Therefore for all x, if y_2 cooks, then y_2 is driving a car.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x) <-> Q(x). Therefore forall x: R(x) -> S(x).