Translate the following inference to logic notation: For all x, x_3 will listen to a song if and only if x_3 will play tennis. For all x, x_3 will listen to a song if and only if x_3 is fast. Therefore for all x, if x_3 were fast, then x_3 is playing tennis.
forall x: P(x) <-> Q(x). forall x: P(x) <-> R(x). Therefore forall x: R(x) -> Q(x).