Translate the following inference to logic notation: For all x, if x takes a plane, then x is a politician. For all x, x will not cook or x will take a plane. If it is cloudy, then David is not a politician. For all x, if x were bored, then x is a politician. For all x, x will cook or x is bored. Therefore it is not cloudy.
forall x: P(x) -> Q(x). forall x: ~R(x) or P(x). p -> ~Q(a). forall x: S(x) -> Q(x). forall x: R(x) or S(x). Therefore ~p.