Translate the following inference to logic notation: For all x, x_2 will not play a game or x_2 will sleep. For all x, x_2 will play a game or x_2 will read a book. For all x, if x_2 reads a book, then x_2 is working. There is at least one x for which if x_2 sleeps, then x_2 is working. Therefore there is at least one x for which x_2 will work.
forall x: ~P(x) or Q(x). forall x: P(x) or R(x). forall x: R(x) -> S(x). exists x: Q(x) -> S(x). Therefore exists x: S(x).