Consider the following premises. If Jennifer drinks water, then Mary is playing tennis. Mary is playing tennis if and only if Jennifer is writing a letter. For all x_8, x_8 will drink water or x_8 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: Mary is not playing tennis.
 From the fact that for all x_8, x_8 will drink water or x_8 will write a letter we can infer that Jennifer is drinking water or Jennifer is writing a letter via universal instantiation. From the fact that Mary is playing tennis if and only if Jennifer is writing a letter we can infer that if Jennifer writes a letter, then Mary is playing tennis via biconditional elimination. Finally, from the fact that if Jennifer drinks water, then Mary is playing tennis, that if Jennifer writes a letter, then Mary is playing tennis, and that Jennifer is drinking water or Jennifer is writing a letter we can infer that Mary is playing tennis via disjunction elimination, which contradicts that Mary is not playing tennis. Therefore, the answer is no.