Translate the following inference to logic notation: For all x, x_9 will listen to a song if and only if x_9 is an electrician. For all x, if x_9 were a police officer, then x_9 is an electrician. There is at least one x for which if x_9 climbs a mountain, then x_9 is a police officer. Therefore there is at least one x for which if x_9 climbs a mountain, then x_9 is listening to a song.
forall x: P(x) <-> Q(x). forall x: R(x) -> Q(x). exists x: S(x) -> R(x). Therefore exists x: S(x) -> P(x).