Translate the following inference to logic notation: For all x, if y_3 works, then y_3 is a police officer. For all x, y_3 will work if and only if y_3 is a police officer. Therefore for all x, if y_3 were a police officer, then y_3 is working.
forall x: P(x) -> Q(x). forall x: P(x) <-> Q(x). Therefore forall x: Q(x) -> P(x).