Translate the following inference to logic notation: For all x, if x_9 listens to a song, then x_9 is a carpenter. For all x, if x_9 were sad, then x_9 is listening to a song. There is at least one x for which x_9 is not a carpenter. For all x, if x_9 listens to a song, then x_9 is sad. Therefore there is at least one x for which x_9 is not sad.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: ~Q(x). forall x: P(x) -> R(x). Therefore exists x: ~R(x).