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