Translate the following inference to logic notation: For all x, if x_10 were a soldier, then x_10 is sleeping. For all x, if x_10 were sad, then x_10 is playing a game. There is at least one x for which x_10 will not sleep. For all x, if x_10 sleeps, then x_10 is sad. For all x, if x_10 plays a game, then x_10 is a soldier. Therefore there is at least one x for which x_10 is not sad.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: ~Q(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). Therefore exists x: ~R(x).