Translate the following inference to logic notation: For all x, if x_5 were a politician, then x_5 is taking a plane. For all x, x_5 will write a letter. For all x, x_5 is a politician. For all x, if x_5 takes a plane, then x_5 is running. Therefore for all x, x_5 will go running and x_5 will write a letter.
forall x: P(x) -> Q(x). forall x: R(x). forall x: P(x). forall x: Q(x) -> S(x). Therefore forall x: S(x) and R(x).