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