Consider the following premises. q_8 <-> r_1. w -> ~r_2. w <-> q_8. r_2. Can we infer r_1 from them? If possible, name the inference rules being used at each step.
 From w -> ~r_2, r_2 we can infer ~w via modus tollens. From w <-> q_8, ~w we can infer ~q_8 via biconditional elimination. From q_8 <-> r_1 we can infer r_1 -> q_8 via biconditional elimination. Finally, from r_1 -> q_8, ~q_8 we can infer ~r_1 via modus tollens, which contradicts r_1. Therefore, the answer is no.