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