Translate the following inference to logic notation: For all x, x_8 will sleep or x_8 is not a police officer. For all x, x_8 is a police officer or x_8 is a janitor. For all x, x_8 will sleep if and only if x_8 is a janitor. Therefore for all x, x_8 will sleep.
forall x: P(x) or ~Q(x). forall x: Q(x) or R(x). forall x: P(x) <-> R(x). Therefore forall x: P(x).