Translate the following inference to logic notation: For all x, if x_10 were a writer, then x_10 is listening to a song. There is at least one x for which x_10 is rich. For all x, if x_10 were rich, then x_10 is a writer. For all x, x_10 is bored. Therefore there is at least one x for which x_10 is bored and x_10 will listen to a song.
forall x: P(x) -> Q(x). exists x: R(x). forall x: R(x) -> P(x). forall x: S(x). Therefore exists x: S(x) and Q(x).