Consider the following premises. Jessica is a politician if and only if Elisabeth is poor. Elisabeth is poor if and only if Richard is taking a plane. Richard is taking a plane or Jessica is a politician. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is poor.
 From the fact that Jessica is a politician if and only if Elisabeth is poor we can infer that if Jessica were a politician, then Elisabeth is poor via biconditional elimination. From the fact that Elisabeth is poor if and only if Richard is taking a plane we can infer that if Richard takes a plane, then Elisabeth is poor via biconditional elimination. Finally, from the fact that if Richard takes a plane, then Elisabeth is poor, that if Jessica were a politician, then Elisabeth is poor, and that Richard is taking a plane or Jessica is a politician we can infer that Elisabeth is poor via disjunction elimination. Therefore, the answer is yes.