Translate the following inference to logic notation: There is at least one x for which x_3 will not cook. For all x, if x_3 were a soldier, then x_3 is cooking. For all x, if x_3 cooks, then x_3 is a soldier. Therefore there is at least one x for which x_3 is not a soldier.
exists x: ~P(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore exists x: ~Q(x).