Translate the following inference to logic notation: There is at least one x for which x_8 will play a game. For all x, if x_8 plays a game, then x_8 is running. For all x, x_8 is sad if and only if x_8 will go running. Therefore there is at least one x for which x_8 is sad.
exists x: P(x). forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). Therefore exists x: R(x).