Consider the following premises. Charles is cooking if and only if Patricia is rich. Charles is running or Susan is a doctor. Charles is not running. Charles is not cooking. Can we infer the following from them? If we can, name the inference rule being used: Patricia is rich.
 From the fact that Charles is running or Susan is a doctor, and that Charles is not running we can infer that Susan is a doctor via disjunctive syllogism. Finally, from the fact that Charles is cooking if and only if Patricia is rich, and that Charles is not cooking we can infer that Patricia is not rich via biconditional elimination, which contradicts that Patricia is rich. Therefore, the answer is no.