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