Translate the following inference to logic notation: For all x, z will listen to a song if and only if z is excited. For all x, z will listen to a song or z is not excited. Therefore for all x, z will listen to a song if and only if z is excited.
forall x: P(x) <-> Q(x). forall x: P(x) or ~Q(x). Therefore forall x: P(x) <-> Q(x).