Translate the following inference to logic notation: For all x, x_2 is a janitor. For all x, if x_2 listens to a song, then x_2 is playing tennis. There is at least one x for which if x_2 were a janitor, then x_2 is listening to a song. Therefore there is at least one x for which x_2 will play tennis.
forall x: P(x). forall x: Q(x) -> R(x). exists x: P(x) -> Q(x). Therefore exists x: R(x).