Translate the following inference to logic notation: For all x, x_10 is not a carpenter. For all x, if x_10 climbs a mountain, then x_10 is a carpenter. There is at least one x for which x_10 will play a game if and only if x_10 will sleep. For all x, x_10 will climb a mountain or x_10 will play a game. Therefore there is at least one x for which x_10 will sleep.
forall x: ~P(x). forall x: Q(x) -> P(x). exists x: R(x) <-> S(x). forall x: Q(x) or R(x). Therefore exists x: S(x).