Consider the following premises. It is raining if and only if Richard is an office clerk. William is a politician or it is raining. If William were a politician, then Richard is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: Richard is not an office clerk.
 From the fact that it is raining if and only if Richard is an office clerk we can infer that if it rains, then Richard is an office clerk via biconditional elimination. Finally, from the fact that if William were a politician, then Richard is an office clerk, that if it rains, then Richard is an office clerk, and that William is a politician or it is raining we can infer that Richard is an office clerk via disjunction elimination, which contradicts that Richard is not an office clerk. Therefore, the answer is no.