Translate the following inference to logic notation: For all x, x_9 will write a letter if and only if x_9 will drive a car. For all x, x_9 is a doctor if and only if x_9 will drive a car. There is at least one x for which if x_9 writes a letter, then x_9 is reading a book. For all x, if x_9 reads a book, then x_9 is writing a letter. For all x, x_9 is not a doctor. Therefore there is at least one x for which x_9 will not read a book.
forall x: P(x) <-> Q(x). forall x: R(x) <-> Q(x). exists x: P(x) -> S(x). forall x: S(x) -> P(x). forall x: ~R(x). Therefore exists x: ~S(x).