Translate the following inference to logic notation: There is at least one x for which if x_8 were fast, then x_8 is listening to a song. For all x, x_8 is not bored. For all x, x_8 is bored if and only if x_8 will listen to a song. Therefore there is at least one x for which x_8 is not fast.
exists x: P(x) -> Q(x). forall x: ~R(x). forall x: R(x) <-> Q(x). Therefore exists x: ~P(x).