Consider the following premises. It is late. Susan is reading a book if and only if Susan is playing squash. Susan is not reading a book. Susan is playing squash or David is running. Can we infer the following from them? If we can, name the inference rule being used: David is not running.
 From the fact that Susan is reading a book if and only if Susan is playing squash, and that Susan is not reading a book we can infer that Susan is not playing squash via biconditional elimination. Finally, from the fact that Susan is playing squash or David is running, and that Susan is not playing squash we can infer that David is running via disjunctive syllogism, which contradicts that David is not running. Therefore, the answer is no.