Translate the following inference to logic notation: There is at least one x for which x_9 will drive a car if and only if x_9 will write a letter. For all x, if x_9 cooks, then x_9 is excited. For all x, if x_9 were excited, then x_9 is writing a letter. Therefore there is at least one x for which if x_9 cooks, then x_9 is driving a car.
exists x: P(x) <-> Q(x). forall x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore exists x: R(x) -> P(x).