Translate the following inference to logic notation: For all x, if x_10 plays a game, then x_10 is cooking. For all x, if x_10 climbs a mountain, then x_10 is cooking. For all x, if x_10 cooks, then x_10 is sleeping. There is at least one x for which x_10 will play a game. Therefore there is at least one x for which x_10 will sleep.
forall x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: Q(x) -> S(x). exists x: P(x). Therefore exists x: S(x).