Translate the following inference to logic notation: For all x, if z listens to a song, then z is making tea. For all x, z is an artist if and only if z will listen to a song. For all x, if z makes tea, then z is an artist. There is at least one x for which z is not an artist. Therefore there is at least one x for which z 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: ~R(x). Therefore exists x: ~P(x).