Translate the following inference to logic notation: For all x, if y cooks, then y is listening to a song. For all x, if y listens to a song, then y is rich. There is at least one x for which if y writes a letter, then y is working. For all x, if y works, then y is cooking. Therefore there is at least one x for which if y writes a letter, then y is rich.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: S(x) -> T(x). forall x: T(x) -> P(x). Therefore exists x: S(x) -> R(x).