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