Translate the following inference to logic notation: There is at least one x for which y_2 will play a game if and only if y_2 will climb a mountain. For all x, y_2 will play a game if and only if y_2 will take a plane. For all x, y_2 will not climb a mountain. Therefore there is at least one x for which y_2 will not take a plane.
exists x: P(x) <-> Q(x). forall x: P(x) <-> R(x). forall x: ~Q(x). Therefore exists x: ~R(x).