Translate the following inference to logic notation: For all x, if x_9 reads a book, then x_9 is happy. For all x, x_9 will sleep or x_9 is rich. For all x, x_9 will not sleep. There is at least one x for which x_9 is happy if and only if x_9 is rich. Therefore there is at least one x for which x_9 is happy.
forall x: P(x) -> Q(x). forall x: R(x) or S(x). forall x: ~R(x). exists x: Q(x) <-> S(x). Therefore exists x: Q(x).