Translate the following inference to logic notation: For all x, if x_5 were sad, then x_5 is climbing a mountain. For all x, x_5 will listen to a song. There is at least one x for which if x_5 climbs a mountain, then x_5 is sad. For all x, if x_5 were sad, then x_5 is not listening to a song. Therefore there is at least one x for which x_5 will not climb a mountain.
forall x: P(x) -> Q(x). forall x: R(x). exists x: Q(x) -> P(x). forall x: P(x) -> ~R(x). Therefore exists x: ~Q(x).