Translate the following inference to logic notation: For all x, if x_11 takes a plane, then x_11 is writing a letter. For all x, if x_11 writes a letter, then x_11 is a server. For all x, x_11 is rich or x_11 is not a server. There is at least one x for which if x_11 were rich, then x_11 is taking a plane. Therefore there is at least one x for which x_11 will write a letter if and only if x_11 will take a plane.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) or ~R(x). exists x: S(x) -> P(x). Therefore exists x: Q(x) <-> P(x).