Consider the following premises. q_8 or ~w_3. q or w_3. q <-> q_8. Can we infer q_8 from them? If possible, name the inference rules being used at each step.
 From q <-> q_8 we can infer q -> q_8 via biconditional elimination. From q_8 or ~w_3 we can infer w_3 -> q_8 via rewriting. Finally, from q -> q_8, w_3 -> q_8, q or w_3 we can infer q_8 via disjunction elimination. Therefore, the answer is yes.