Translate the following inference to logic notation: There is at least one x for which x_8 will play a game or x_8 will climb a mountain. For all x, x_8 will not play a game. For all x, x_8 will climb a mountain if and only if x_8 is poor. Therefore there is at least one x for which x_8 is poor.
exists x: P(x) or Q(x). forall x: ~P(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x).