Consider the following premises. There is at least one x_3 for which x_3 is not a sailor. For all x_3, if x_3 writes a letter, then x_3 is a sailor. For all x_3, x_3 will write a letter or x_3 is not a sailor. Can we infer the following from them? For all x_3, x_3 will write a letter.
 From the fact that for all x_3, x_3 will write a letter or x_3 is not a sailor we can infer that for all x_3, if x_3 were a sailor, then x_3 is writing a letter. From the fact that for all x_3, if x_3 writes a letter, then x_3 is a sailor, and that for all x_3, if x_3 were a sailor, then x_3 is writing a letter we can infer that for all x_3, x_3 will write a letter if and only if x_3 is a sailor. Finally, from the fact that for all x_3, x_3 will write a letter if and only if x_3 is a sailor, and that there is at least one x_3 for which x_3 is not a sailor we can infer that there is at least one x_3 for which x_3 will not write a letter, which contradicts that For all x_3, x_3 will write a letter. Therefore, the answer is no.