Consider the following premises. It is snowing. William is a cashier or it is not snowing. If William were a cashier, then it is raining. Can we infer the following from them? It is not raining.
 From the fact that William is a cashier or it is not snowing we can infer that if it snows, then William is a cashier. From the fact that if it snows, then William is a cashier, and that it is snowing we can infer that William is a cashier. Finally, from the fact that if William were a cashier, then it is raining, and that William is a cashier we can infer that it is raining, which contradicts that It is not raining. Therefore, the answer is no.