Consider the following premises. If Karen works, then Jessica is happy. Patricia is not a nurse. If Jessica were happy, then Karen is working. If Patricia were a nurse, then Jessica is happy. Jessica is happy if and only if Patricia is a nurse. Can we infer the following from them? If we can, name the inference rule being used: Karen is working.
 From the fact that Jessica is happy if and only if Patricia is a nurse we can infer that if Jessica were happy, then Patricia is a nurse via biconditional elimination. From the fact that if Jessica were happy, then Patricia is a nurse, and that if Patricia were a nurse, then Jessica is happy we can infer that Jessica is happy if and only if Patricia is a nurse via biconditional introduction. From the fact that Jessica is happy if and only if Patricia is a nurse, and that Patricia is not a nurse we can infer that Jessica is not happy via biconditional elimination. From the fact that if Jessica were happy, then Karen is working, and that if Karen works, then Jessica is happy we can infer that Jessica is happy if and only if Karen is working via biconditional introduction. Finally, from the fact that Jessica is happy if and only if Karen is working, and that Jessica is not happy we can infer that Karen is not working via biconditional elimination, which contradicts that Karen is working. Therefore, the answer is no.