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