Translate the following inference to logic notation: For all x, x will not write a letter. For all x, if x were an astronaut, then x is writing a letter. For all x, if x goes running, then x is taking a plane. For all x, if x takes a plane, then x is running. For all x, x will go running if and only if x is an astronaut. Therefore for all x, x will not take a plane.
forall x: ~P(x). forall x: Q(x) -> P(x). forall x: R(x) -> S(x). forall x: S(x) -> R(x). forall x: R(x) <-> Q(x). Therefore forall x: ~S(x).