Translate the following inference to logic notation: For all x, x_9 will listen to a song if and only if x_9 will climb a mountain. If Jessica climbs a mountain, then Jessica is listening to a song. Therefore if Jessica climbs a mountain, then Jessica is listening to a song.
forall x: P(x) <-> Q(x). Q(a) -> P(a). Therefore Q(a) -> P(a).