Translate the following inference to logic notation: For all x, x is a police officer if and only if x will go running. There is at least one x for which x is a police officer or x will not go running. Therefore there is at least one x for which if x were a police officer, then x is running.
forall x: P(x) <-> Q(x). exists x: P(x) or ~Q(x). Therefore exists x: P(x) -> Q(x).