Translate the following inference to logic notation: For all x, if x_10 listens to a song, then x_10 is writing a letter. For all x, if x_10 writes a letter, then x_10 is listening to a song. For all x, x_10 will write a letter if and only if x_10 is rich. For all x, if x_10 writes a letter, then x_10 is listening to a song. For all x, x_10 is not rich. Therefore for all x, x_10 will not listen to a song.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) <-> R(x). forall x: Q(x) -> P(x). forall x: ~R(x). Therefore forall x: ~P(x).