Translate the following inference to logic notation: For all x, x_6 is a scientist. For all x, if x_6 were a janitor, then x_6 is a police officer. For all x, x_6 will write a letter. For all x, if x_6 writes a letter, then x_6 is a janitor. Therefore for all x, x_6 is a police officer.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x). forall x: S(x) -> Q(x). Therefore forall x: R(x).