Translate the following inference to logic notation: For all x, if x_9 were an artist, then x_9 is cooking. For all x, if x_9 cooks, then x_9 is an artist. For all x, x_9 will drink water if and only if x_9 will cook. There is at least one x for which x_9 will not drink water. Therefore there is at least one x for which x_9 is not an artist.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: R(x) <-> Q(x). exists x: ~R(x). Therefore exists x: ~P(x).