Consider the following premises. There is at least one x_6 for which x_6 is bored and x_6 will cook. For all x_6, x_6 will read a book. Can we infer the following from them? There is at least one x_6 for which x_6 is bored and x_6 will read a book.
 From the fact that there is at least one x_6 for which x_6 is bored and x_6 will cook we can infer that there is at least one x_6 for which x_6 is bored. Finally, from the fact that there is at least one x_6 for which x_6 is bored, and that for all x_6, x_6 will read a book we can infer that there is at least one x_6 for which x_6 is bored and x_6 will read a book. Therefore, the answer is yes.