Translate the following inference to logic notation: For all x, if x_9 cooks, then x_9 is listening to a song. For all x, if x_9 makes tea, then x_9 is listening to a song. For all x, x_9 will cook. There is at least one x for which if x_9 listens to a song, then x_9 is making tea. Therefore there is at least one x for which x_9 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: P(x). exists x: Q(x) -> R(x). Therefore exists x: Q(x).