Translate the following inference to logic notation: For all x, x_10 will climb a mountain if and only if x_10 will play a game. There is at least one x for which x_10 will play a game if and only if x_10 will climb a mountain. Therefore there is at least one x for which if x_10 plays a game, then x_10 is climbing a mountain.
forall x: P(x) <-> Q(x). exists x: Q(x) <-> P(x). Therefore exists x: Q(x) -> P(x).