Translate the following inference to logic notation: For all x, if x_6 were a bartender, then x_6 is playing tennis. For all x, if x_6 plays tennis, then x_6 is taking a plane. For all x, if x_6 were fast, then x_6 is a bartender. There is at least one x for which if x_6 takes a plane, then x_6 is fast. Therefore there is at least one x for which x_6 is fast if and only if x_6 will play tennis.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). exists x: R(x) -> S(x). Therefore exists x: S(x) <-> Q(x).