Translate the following inference to logic notation: For all x, z_1 is not a bartender. For all x, if z_1 were a lawyer, then z_1 is a bartender. There is at least one x for which z_1 is a bartender if and only if z_1 is a lawyer. Therefore there is at least one x for which z_1 is not a lawyer.
forall x: ~P(x). forall x: Q(x) -> P(x). exists x: P(x) <-> Q(x). Therefore exists x: ~Q(x).