Consider the following premises. For all x_2, x_2 will not cook. For all x_2, if x_2 drinks water, then x_2 is playing squash. For all x_2, if x_2 plays squash, then x_2 is cooking. For all x_2, if x_2 cooks, then x_2 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 will not drink water.
 From the fact that for all x_2, if x_2 drinks water, then x_2 is playing squash, and that for all x_2, if x_2 plays squash, then x_2 is cooking we can infer that for all x_2, if x_2 drinks water, then x_2 is cooking via universal transitivity. From the fact that for all x_2, if x_2 cooks, then x_2 is drinking water, and that for all x_2, if x_2 drinks water, then x_2 is cooking we can infer that for all x_2, x_2 will cook if and only if x_2 will drink water via universal biconditional introduction. Finally, from the fact that for all x_2, x_2 will cook if and only if x_2 will drink water, and that for all x_2, x_2 will not cook we can infer that for all x_2, x_2 will not drink water via universal biconditional elimination. Therefore, the answer is yes.