Consider the following premises. It is raining if and only if Barbara is a cashier. Robert is a janitor if and only if Barbara is a cashier. For all z, z is not a janitor. Can we infer the following from them? It is raining.
 From the fact that for all z, z is not a janitor we can infer that Robert is not a janitor. From the fact that Robert is a janitor if and only if Barbara is a cashier, and that Robert is not a janitor we can infer that Barbara is not a cashier. Finally, from the fact that it is raining if and only if Barbara is a cashier, and that Barbara is not a cashier we can infer that it is not raining, which contradicts that It is raining. Therefore, the answer is no.