Translate the following inference to logic notation: For all x, if x_8 were a politician, then x_8 is cooking. There is at least one x for which x_8 is a politician or x_8 will not cook. For all x, if x_8 cooks, then x_8 is working. For all x, x_8 will not work. Therefore there is at least one x for which x_8 is not a politician.
forall x: P(x) -> Q(x). exists x: P(x) or ~Q(x). forall x: Q(x) -> R(x). forall x: ~R(x). Therefore exists x: ~P(x).