Consider the following premises. David is not sleeping. For all x_8, if x_8 plays tennis, then x_8 is sleeping. For all x_8, if x_8 sleeps, then x_8 is playing tennis. David is playing tennis or Linda is a scientist. Can we infer the following from them? If we can, name the inference rule being used: Linda is not a scientist.
 From the fact that for all x_8, if x_8 sleeps, then x_8 is playing tennis, and that for all x_8, if x_8 plays tennis, then x_8 is sleeping we can infer that for all x_8, x_8 will sleep if and only if x_8 will play tennis via universal biconditional introduction. From the fact that for all x_8, x_8 will sleep if and only if x_8 will play tennis we can infer that David is sleeping if and only if David is playing tennis via universal instantiation. From the fact that David is sleeping if and only if David is playing tennis, and that David is not sleeping we can infer that David is not playing tennis via biconditional elimination. Finally, from the fact that David is playing tennis or Linda is a scientist, and that David is not playing tennis we can infer that Linda is a scientist via disjunctive syllogism, which contradicts that Linda is not a scientist. Therefore, the answer is no.