Translate the following inference to logic notation: For all x, z will read a book if and only if z will write a letter. There is at least one x for which if z writes a letter, then z is reading a book. Therefore there is at least one x for which if z reads a book, then z is writing a letter.
forall x: P(x) <-> Q(x). exists x: Q(x) -> P(x). Therefore exists x: P(x) -> Q(x).