Translate the following inference to logic notation: For all x, x_6 is not a politician or x_6 will go running. For all x, if x_6 goes running, then x_6 is cooking. For all x, x_6 is a politician or x_6 is rich. For all x, x_6 will cook if and only if x_6 is rich. Therefore for all x, x_6 will cook.
forall x: ~P(x) or Q(x). forall x: Q(x) -> R(x). forall x: P(x) or S(x). forall x: R(x) <-> S(x). Therefore forall x: R(x).