Translate the following inference to logic notation: For all x, if y drives a car, then y is listening to a song. For all x, if y reads a book, then y is listening to a song. For all x, if y were a politician, then y is not listening to a song. There is at least one x for which y will read a book. Therefore there is at least one x for which y is not a politician.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: S(x) -> ~Q(x). exists x: R(x). Therefore exists x: ~S(x).