Consider the following premises. q_3 -> r. q_3 <-> r_2. ~r. Can we infer ~r_2 from them? If possible, name the inference rules being used at each step.
 From q_3 -> r, ~r we can infer ~q_3 via modus tollens. Finally, from q_3 <-> r_2, ~q_3 we can infer ~r_2 via biconditional elimination. Therefore, the answer is yes.