Consider the following premises. It is snowing or Jennifer is playing tennis. For all y, y will play tennis if and only if y will cook. If it snows, then Jennifer is cooking. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not cooking.
 From the fact that for all y, y will play tennis if and only if y will cook we can infer that Jennifer is playing tennis if and only if Jennifer is cooking via universal instantiation. From the fact that Jennifer is playing tennis if and only if Jennifer is cooking we can infer that if Jennifer plays tennis, then Jennifer is cooking via biconditional elimination. Finally, from the fact that if it snows, then Jennifer is cooking, that if Jennifer plays tennis, then Jennifer is cooking, and that it is snowing or Jennifer is playing tennis we can infer that Jennifer is cooking via disjunction elimination, which contradicts that Jennifer is not cooking. Therefore, the answer is no.