Translate the following inference to logic notation: For all x, x_2 is excited. For all x, if x_2 takes a plane, then x_2 is a taxi driver. There is at least one x for which if x_2 were excited, then x_2 is taking a plane. Therefore there is at least one x for which x_2 is a taxi driver.
forall x: P(x). forall x: Q(x) -> R(x). exists x: P(x) -> Q(x). Therefore exists x: R(x).