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