Translate the following inference to logic notation: For all x, if x_7 listens to a song, then x_7 is sleeping. For all x, x_7 will listen to a song if and only if x_7 will sleep. Therefore if Richard listens to a song, then Richard is sleeping.
forall x: P(x) -> Q(x). forall x: P(x) <-> Q(x). Therefore P(a) -> Q(a).