Consider the following premises. Elisabeth is writing a letter if and only if Jennifer is an office clerk. For all x_14, if x_14 makes tea, then x_14 is reading a book. For all x_14, if x_14 were bored, then x_14 is making tea. For all x_14, x_14 is an office clerk if and only if x_14 is bored. For all x_14, x_14 will not read a book. 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 for all x_14, if x_14 makes tea, then x_14 is reading a book, and that for all x_14, x_14 will not read a book we can infer that for all x_14, x_14 will not make tea via universal modus tollens. From the fact that for all x_14, if x_14 were bored, then x_14 is making tea, and that for all x_14, x_14 will not make tea we can infer that for all x_14, x_14 is not bored via universal modus tollens. From the fact that for all x_14, x_14 is an office clerk if and only if x_14 is bored, and that for all x_14, x_14 is not bored we can infer that for all x_14, x_14 is not an office clerk via universal biconditional elimination. From the fact that for all x_14, x_14 is not an office clerk we can infer that Jennifer is not an office clerk via universal instantiation. Finally, from the fact that Elisabeth is writing a letter if and only if Jennifer is an office clerk, and that Jennifer is not an office clerk we can infer that Elisabeth is not writing a letter via biconditional elimination. Therefore, the answer is yes.