Consider the following premises. For all x_11, x_11 will not play tennis or x_11 will write a letter. For all x_11, x_11 is not happy. There is at least one x_11 for which x_11 will play tennis or x_11 is happy. Can we infer the following from them? There is at least one x_11 for which x_11 will write a letter or x_11 will climb a mountain.
 From the fact that there is at least one x_11 for which x_11 will play tennis or x_11 is happy, and that for all x_11, x_11 will not play tennis or x_11 will write a letter we can infer that there is at least one x_11 for which x_11 is happy or x_11 will write a letter. From the fact that there is at least one x_11 for which x_11 is happy or x_11 will write a letter, and that for all x_11, x_11 is not happy we can infer that there is at least one x_11 for which x_11 will write a letter. Finally, from the fact that there is at least one x_11 for which x_11 will write a letter we can infer that there is at least one x_11 for which x_11 will write a letter or x_11 will climb a mountain. Therefore, the answer is yes.