Translate the following inference to logic notation: For all x, if x_5 works, then x_5 is a police officer. There is at least one x for which x_5 is sad if and only if x_5 will listen to a song. For all x, if x_5 listens to a song, then x_5 is working. For all x, x_5 is not a police officer. Therefore there is at least one x for which x_5 is not sad.
forall x: P(x) -> Q(x). exists x: R(x) <-> S(x). forall x: S(x) -> P(x). forall x: ~Q(x). Therefore exists x: ~R(x).