Consider the following premises. r. r_1 <-> p_2. p_2 -> ~r. Can we infer ~r_1 from them? If possible, name the inference rules being used at each step.
 From p_2 -> ~r, r we can infer ~p_2 via modus tollens. Finally, from r_1 <-> p_2, ~p_2 we can infer ~r_1 via biconditional elimination. Therefore, the answer is yes.