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