Translate the following inference to logic notation: For all x, if x_6 were a janitor, then x_6 is a police officer. There is at least one x for which if x_6 were a police officer, then x_6 is taking a plane. For all x, x_6 will take a plane if and only if x_6 is a janitor. Therefore there is at least one x for which x_6 is a janitor if and only if x_6 will take a plane.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: R(x) <-> P(x). Therefore exists x: P(x) <-> R(x).