Translate the following inference to logic notation: For all x, if x_9 plays tennis, then x_9 is fast. For all x, if x_9 were a writer, then x_9 is working. For all x, if x_9 works, then x_9 is playing tennis. For all x, x_9 is a writer if and only if x_9 is fast. Therefore for all x, x_9 is a writer if and only if x_9 will work.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). forall x: R(x) <-> Q(x). Therefore forall x: R(x) <-> S(x).