Translate the following inference to logic notation: For all x, x_12 will not make tea. There is at least one x for which x_12 will drink water if and only if x_12 will write a letter. For all x, x_12 will play a game if and only if x_12 will drink water. For all x, x_12 will make tea if and only if x_12 will play a game. Therefore there is at least one x for which x_12 will not write a letter.
forall x: ~P(x). exists x: Q(x) <-> R(x). forall x: S(x) <-> Q(x). forall x: P(x) <-> S(x). Therefore exists x: ~R(x).