Consider the following premises. Linda is writing a letter if and only if Jessica is running. Linda is not writing a letter. For all x_2, x_2 will go running if and only if x_2 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: Jessica is an office clerk.
 From the fact that for all x_2, x_2 will go running if and only if x_2 is an office clerk we can infer that for all x_2, if x_2 were an office clerk, then x_2 is running via universal biconditional elimination. From the fact that for all x_2, if x_2 were an office clerk, then x_2 is running we can infer that if Jessica were an office clerk, then Jessica is running via universal instantiation. From the fact that Linda is writing a letter if and only if Jessica is running, and that Linda is not writing a letter we can infer that Jessica is not running via biconditional elimination. Finally, from the fact that if Jessica were an office clerk, then Jessica is running, and that Jessica is not running we can infer that Jessica is not an office clerk via modus tollens, which contradicts that Jessica is an office clerk. Therefore, the answer is no.