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