Translate the following inference to logic notation: For all x, if x_1 were an artist, then x_1 is running. There is at least one x for which x_1 will not go running. For all x, x_1 is an artist if and only if x_1 will go running. Therefore there is at least one x for which x_1 is not an artist.
forall x: P(x) -> Q(x). exists x: ~Q(x). forall x: P(x) <-> Q(x). Therefore exists x: ~P(x).