Translate the following inference to logic notation: There is at least one x for which if x cooks, then x is listening 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 cook if and only if x will listen to a song.
exists x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore exists x: P(x) <-> Q(x).