Translate the following inference to logic notation: There is at least one x for which z_2 is a bartender if and only if z_2 is an artist. For all x, z_2 will take a plane if and only if z_2 is an artist. For all x, z_2 is a politician. For all x, if z_2 takes a plane, then z_2 is not a politician. Therefore there is at least one x for which z_2 is not a bartender.
exists x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). forall x: S(x). forall x: R(x) -> ~S(x). Therefore exists x: ~P(x).