Translate the following inference to logic notation: For all x, if x_1 were an office clerk, then x_1 is a police officer. For all x, if x_1 were a cashier, then x_1 is an office clerk. For all x, if x_1 were a police officer, then x_1 is a cashier. For all x, x_1 is a police officer or x_1 is not an office clerk. Therefore for all x, x_1 is an office clerk if and only if x_1 is a police officer.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). forall x: Q(x) or ~P(x). Therefore forall x: P(x) <-> Q(x).