Consider the following premises. For all x_3, x_3 will cook or x_3 will sleep. There is at least one x_3 for which if x_3 cooks, then x_3 is working. For all x_3, x_3 will sleep if and only if x_3 will work. Can we infer the following from them? There is at least one x_3 for which x_3 will work.
 From the fact that for all x_3, x_3 will sleep if and only if x_3 will work we can infer that for all x_3, if x_3 sleeps, then x_3 is working. Finally, from the fact that there is at least one x_3 for which if x_3 cooks, then x_3 is working, that for all x_3, if x_3 sleeps, then x_3 is working, and that for all x_3, x_3 will cook or x_3 will sleep we can infer that there is at least one x_3 for which x_3 will work. Therefore, the answer is yes.