Translate the following inference to logic notation: For all x, z will write a letter or z is not a bartender. For all x, z will write a letter if and only if z is a bartender. Therefore for all x, z is a bartender if and only if z will write a letter.
forall x: P(x) or ~Q(x). forall x: P(x) <-> Q(x). Therefore forall x: Q(x) <-> P(x).