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