Consider the following premises. There is at least one z for which z will climb a mountain or z will play tennis. For all z, z will climb a mountain if and only if z is happy. For all z, z is not happy. Can we infer the following from them? For all z, z will not play tennis.
 From the fact that for all z, z will climb a mountain if and only if z is happy, and that for all z, z is not happy we can infer that for all z, z will not climb a mountain. Finally, from the fact that there is at least one z for which z will climb a mountain or z will play tennis, and that for all z, z will not climb a mountain we can infer that there is at least one z for which z will play tennis, which contradicts that For all z, z will not play tennis. Therefore, the answer is no.