Translate the following inference to logic notation: For all x, x_11 will listen to a song if and only if x_11 will climb a mountain. For all x, x_11 will listen to a song if and only if x_11 will climb a mountain. Therefore if Elisabeth climbs a mountain, then Elisabeth is listening to a song.
forall x: P(x) <-> Q(x). forall x: P(x) <-> Q(x). Therefore Q(a) -> P(a).