Translate the following inference to logic notation: For all x, if x_8 takes a plane, then x_8 is a police officer. For all x, if x_8 were a janitor, then x_8 is taking a plane. There is at least one x for which x_8 will write a letter or x_8 is not a police officer. Therefore there is at least one x for which if x_8 were a janitor, then x_8 is writing a letter.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: S(x) or ~Q(x). Therefore exists x: R(x) -> S(x).