Translate the following inference to logic notation: For all x, if x_6 were excited, then x_6 is a writer. For all x, x_6 is fast. For all x, if x_6 were a writer, then x_6 is not fast. There is at least one x for which x_6 is excited if and only if x_6 will listen to a song. Therefore there is at least one x for which x_6 will not listen to a song.
forall x: P(x) -> Q(x). forall x: R(x). forall x: Q(x) -> ~R(x). exists x: P(x) <-> S(x). Therefore exists x: ~S(x).