Consider the following premises. Karen is drinking water if and only if Elisabeth is a soldier. William is cooking or Elisabeth is a soldier. William is cooking if and only if Karen is drinking water. Can we infer the following from them? If we can, name the inference rule being used: Karen is not drinking water.
 From the fact that William is cooking if and only if Karen is drinking water we can infer that if William cooks, then Karen is drinking water via biconditional elimination. From the fact that Karen is drinking water if and only if Elisabeth is a soldier we can infer that if Elisabeth were a soldier, then Karen is drinking water via biconditional elimination. Finally, from the fact that if William cooks, then Karen is drinking water, that if Elisabeth were a soldier, then Karen is drinking water, and that William is cooking or Elisabeth is a soldier we can infer that Karen is drinking water via disjunction elimination, which contradicts that Karen is not drinking water. Therefore, the answer is no.