Translate the following inference to logic notation: For all x, z is fast if and only if z will listen to a song. For all x, z will listen to a song if and only if z is fast. Therefore for all x, z will listen to a song if and only if z is fast.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore forall x: Q(x) <-> P(x).