Consider the following premises. For all x_12, x_12 will read a book if and only if x_12 will play tennis. Jennifer is playing tennis if and only if Michael is playing squash. For all x_12, x_12 will work if and only if x_12 will read a book. For all x_12, x_12 will not work. Can we infer the following from them? If we can, name the inference rule being used: Michael is playing squash.
 From the fact that for all x_12, x_12 will work if and only if x_12 will read a book, and that for all x_12, x_12 will not work we can infer that for all x_12, x_12 will not read a book via universal biconditional elimination. From the fact that for all x_12, x_12 will read a book if and only if x_12 will play tennis, and that for all x_12, x_12 will not read a book we can infer that for all x_12, x_12 will not play tennis via universal biconditional elimination. From the fact that for all x_12, x_12 will not play tennis we can infer that Jennifer is not playing tennis via universal instantiation. Finally, from the fact that Jennifer is playing tennis if and only if Michael is playing squash, and that Jennifer is not playing tennis we can infer that Michael is not playing squash via biconditional elimination, which contradicts that Michael is playing squash. Therefore, the answer is no.