Translate the following inference to logic notation: For all x, x_1 will play tennis. For all x, if x_1 writes a letter, then x_1 is listening to a song. There is at least one x for which if x_1 plays tennis, then x_1 is listening to a song. Therefore there is at least one x for which x_1 will listen to a song.
forall x: P(x). forall x: Q(x) -> R(x). exists x: P(x) -> R(x). Therefore exists x: R(x).