Translate the following inference to logic notation: There is at least one x for which if x_6 cooks, then x_6 is a bartender. For all x, x_6 will not cook. For all x, if x_6 were a bartender, then x_6 is cooking. Therefore there is at least one x for which x_6 is not a bartender.
exists x: P(x) -> Q(x). forall x: ~P(x). forall x: Q(x) -> P(x). Therefore exists x: ~Q(x).