Translate the following inference to logic notation: For all x, if x plays tennis, then x is rich. For all x, if x listens to a song, then x is playing tennis. There is at least one x for which x will listen to a song if and only if x is rich. Therefore there is at least one x for which x will listen to a song if and only if x is rich.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: R(x) <-> Q(x). Therefore exists x: R(x) <-> Q(x).