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