Translate the following inference to logic notation: For all x, if x_5 writes a letter, then x_5 is working. For all x, if x_5 reads a book, then x_5 is rich. There is at least one x for which if x_5 listens to a song, then x_5 is not working. For all x, x_5 will write a letter or x_5 will read a book. For all x, if x_5 were rich, then x_5 is working. Therefore there is at least one x for which x_5 will not listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: T(x) -> ~Q(x). forall x: P(x) or R(x). forall x: S(x) -> Q(x). Therefore exists x: ~T(x).