Translate the following inference to logic notation: There is at least one x for which x_9 will take a plane if and only if x_9 is a lawyer. For all x, x_9 is a lawyer if and only if x_9 is a bartender. Therefore there is at least one x for which if x_9 were a bartender, then x_9 is taking a plane.
exists x: P(x) <-> Q(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x) -> P(x).