Consider the following premises. If it is windy, then William is reading a book. It is windy if and only if Elisabeth is writing a letter. Richard is not climbing a mountain. If it is windy, then Richard is climbing a mountain. If William reads a book, then Elisabeth is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not writing a letter.
 From the fact that it is windy if and only if Elisabeth is writing a letter we can infer that if Elisabeth writes a letter, then it is windy via biconditional elimination. From the fact that if it is windy, then William is reading a book, and that if William reads a book, then Elisabeth is writing a letter we can infer that if it is windy, then Elisabeth is writing a letter via transitivity. From the fact that if Elisabeth writes a letter, then it is windy, and that if it is windy, then Elisabeth is writing a letter we can infer that Elisabeth is writing a letter if and only if it is windy via biconditional introduction. From the fact that if it is windy, then Richard is climbing a mountain, and that Richard is not climbing a mountain we can infer that it is not windy via modus tollens. Finally, from the fact that Elisabeth is writing a letter if and only if it is windy, and that it is not windy we can infer that Elisabeth is not writing a letter via biconditional elimination. Therefore, the answer is yes.