Consider the following premises. Jessica is a cashier if and only if Patricia is bored. Jessica is a cashier or Richard is not poor. Can we infer the following from them? The fact that Richard were poor does not imply that Patricia is bored.
 From the fact that Jessica is a cashier or Richard is not poor we can infer that if Richard were poor, then Jessica is a cashier. From the fact that Jessica is a cashier if and only if Patricia is bored we can infer that if Jessica were a cashier, then Patricia is bored. Finally, from the fact that if Richard were poor, then Jessica is a cashier, and that if Jessica were a cashier, then Patricia is bored we can infer that if Richard were poor, then Patricia is bored, which contradicts that The fact that Richard were poor does not imply that Patricia is bored. Therefore, the answer is no.