Consider the following premises. For all x, x is a cashier if and only if x is poor. For all x, x is poor or x will sleep. There is at least one x for which x is not a cashier. Can we infer the following from them? There is at least one x for which x will sleep.
 From the fact that for all x, x is a cashier if and only if x is poor, and that there is at least one x for which x is not a cashier we can infer that there is at least one x for which x is not poor. Finally, from the fact that for all x, x is poor or x will sleep, and that there is at least one x for which x is not poor we can infer that there is at least one x for which x will sleep. Therefore, the answer is yes.