Translate the following inference to logic notation: For all x, if y_1 were sad, then y_1 is listening to a song. For all x, if y_1 goes running, then y_1 is sad. For all x, if y_1 listens to a song, then y_1 is running. There is at least one x for which y_1 is not sad. Therefore there is at least one x for which y_1 will not listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). exists x: ~P(x). Therefore exists x: ~Q(x).