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