Translate the following inference to logic notation: For all x, if x_5 were a janitor, then x_5 is a writer. For all x, if x_5 were a writer, then x_5 is a politician. For all x, x_5 will go running if and only if x_5 is a janitor. Therefore for all x, if x_5 goes running, then x_5 is a politician.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: S(x) <-> P(x). Therefore forall x: S(x) -> R(x).