Translate the following inference to logic notation: For all x, x_9 will listen to a song if and only if x_9 is a politician. There is at least one x for which x_9 will not listen to a song. For all x, if x_9 writes a letter, then x_9 is poor. For all x, if x_9 were poor, then x_9 is a politician. Therefore there is at least one x for which x_9 will not write a letter.
forall x: P(x) <-> Q(x). exists x: ~P(x). forall x: R(x) -> S(x). forall x: S(x) -> Q(x). Therefore exists x: ~R(x).