Consider the following premises. It is snowing or Barbara is taking a plane. Barbara is excited if and only if Richard is cooking. If it snows, then James is writing a letter. If Barbara takes a plane, then James is writing a letter. Richard is not cooking. Can we infer the following from them? If we can, name the inference rule being used: James is not writing a letter.
 From the fact that Barbara is excited if and only if Richard is cooking, and that Richard is not cooking we can infer that Barbara is not excited via biconditional elimination. Finally, from the fact that if it snows, then James is writing a letter, that if Barbara takes a plane, then James is writing a letter, and that it is snowing or Barbara is taking a plane we can infer that James is writing a letter via disjunction elimination, which contradicts that James is not writing a letter. Therefore, the answer is no.