Translate the following inference to logic notation: For all x, x_11 will sleep if and only if x_11 will read a book. For all x, x_11 is not bored. For all x, x_11 is bored if and only if x_11 is a scientist. There is at least one x for which if x_11 reads a book, then x_11 is a scientist. Therefore there is at least one x for which x_11 will not sleep.
forall x: P(x) <-> Q(x). forall x: ~R(x). forall x: R(x) <-> S(x). exists x: Q(x) -> S(x). Therefore exists x: ~P(x).