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