Translate the following inference to logic notation: For all x, if y were a taxi driver, then y is a bartender. There is at least one x for which if y were a bartender, then y is a taxi driver. For all x, if y were a bartender, then y is a taxi driver. Therefore there is at least one x for which y is a taxi driver if and only if y is a bartender.
forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) <-> Q(x).