Translate the following inference to logic notation: For all x, z is fast if and only if z will read a book. For all x, z is fast if and only if z will read a book. Therefore for all x, if z were fast, then z is reading a book.
forall x: P(x) <-> Q(x). forall x: P(x) <-> Q(x). Therefore forall x: P(x) -> Q(x).