Translate the following inference to logic notation: For all x, if x_7 were a doctor, then x_7 is cooking. For all x, if x_7 cooks, then x_7 is a doctor. There is at least one x for which if x_7 were a doctor, then x_7 is cooking. For all x, x_7 is not a doctor. Therefore there is at least one x for which x_7 will not cook.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: P(x) -> Q(x). forall x: ~P(x). Therefore exists x: ~Q(x).