Translate the following inference to logic notation: For all x, if x drinks water, then x is cooking. For all x, x will drink water if and only if x will read a book. For all x, x will not drink water. There is at least one x for which x will play a game if and only if x will read a book. For all x, if x cooks, then x is reading a book. Therefore there is at least one x for which x will not play a game.
forall x: P(x) -> Q(x). forall x: P(x) <-> R(x). forall x: ~P(x). exists x: S(x) <-> R(x). forall x: Q(x) -> R(x). Therefore exists x: ~S(x).