Consider the following premises. For all x_14, x_14 will drink water. There is at least one x_14 for which x_14 will go running if and only if x_14 will drink water. Can we infer the following from them? There is at least one x_14 for which x_14 will go running or x_14 will write a letter.
 From the fact that there is at least one x_14 for which x_14 will go running if and only if x_14 will drink water we can infer that there is at least one x_14 for which if x_14 drinks water, then x_14 is running. From the fact that there is at least one x_14 for which if x_14 drinks water, then x_14 is running, and that for all x_14, x_14 will drink water we can infer that there is at least one x_14 for which x_14 will go running. Finally, from the fact that there is at least one x_14 for which x_14 will go running we can infer that there is at least one x_14 for which x_14 will go running or x_14 will write a letter. Therefore, the answer is yes.