Translate the following inference to logic notation: For all x, x_12 is sad if and only if x_12 will drive a car. For all x, x_12 is poor if and only if x_12 will listen to a song. For all x, if x_12 were poor, then x_12 is listening to a song. For all x, x_12 is poor if and only if x_12 will drive a car. For all x, x_12 is not sad. Therefore for all x, x_12 will not listen to a song.
forall x: P(x) <-> Q(x). forall x: R(x) <-> S(x). forall x: R(x) -> S(x). forall x: R(x) <-> Q(x). forall x: ~P(x). Therefore forall x: ~S(x).