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