Translate the following inference to logic notation: For all x, if x_12 plays a game, then x_12 is running. For all x, x_12 will climb a mountain if and only if x_12 will go running. For all x, x_12 will play a game if and only if x_12 is poor. For all x, x_12 will climb a mountain or x_12 is poor. Therefore for all x, x_12 will go running.
forall x: P(x) -> Q(x). forall x: R(x) <-> Q(x). forall x: P(x) <-> S(x). forall x: R(x) or S(x). Therefore forall x: Q(x).