Translate the following inference to logic notation: There is at least one x for which y will not drive a car. For all x, if y were a soldier, then y is listening to a song. For all x, if y listens to a song, then y is a soldier. For all x, y will drive a car if and only if y will listen to a song. Therefore there is at least one x for which y is not a soldier.
exists x: ~P(x). forall x: Q(x) -> R(x). forall x: R(x) -> Q(x). forall x: P(x) <-> R(x). Therefore exists x: ~Q(x).