Consider the following premises. p_1 -> s. ~s. q_11 -> w_1. p_1 <-> w_1. w_1 -> q_11. Can we infer q_11 from them? If possible, name the inference rules being used at each step.
 From w_1 -> q_11, q_11 -> w_1 we can infer w_1 <-> q_11 via biconditional introduction. From p_1 -> s, ~s we can infer ~p_1 via modus tollens. From p_1 <-> w_1, ~p_1 we can infer ~w_1 via biconditional elimination. Finally, from w_1 <-> q_11, ~w_1 we can infer ~q_11 via biconditional elimination, which contradicts q_11. Therefore, the answer is no.