Translate the following inference to logic notation: There is at least one x for which y is not an artist. For all x, if y listens to a song, then y is an artist. For all x, if y were an artist, then y is listening to a song. For all x, y will play tennis if and only if y will listen to a song. Therefore there is at least one x for which y will not play tennis.
exists x: ~P(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). Therefore exists x: ~R(x).