Translate the following inference to logic notation: For all x, if z_3 were a politician, then z_3 is a janitor. There is at least one x for which z_3 is a janitor if and only if z_3 is a politician. For all x, z_3 is not a janitor. Therefore there is at least one x for which z_3 is not a politician.
forall x: P(x) -> Q(x). exists x: Q(x) <-> P(x). forall x: ~Q(x). Therefore exists x: ~P(x).