Translate the following inference to logic notation: For all x, x_9 is not a soldier. For all x, x_9 will play a game or x_9 will work. For all x, if x_9 writes a letter, then x_9 is a soldier. There is at least one x for which x_9 will play a game if and only if x_9 will write a letter. Therefore there is at least one x for which x_9 will work.
forall x: ~P(x). forall x: Q(x) or R(x). forall x: S(x) -> P(x). exists x: Q(x) <-> S(x). Therefore exists x: R(x).