Consider the following premises. w_2 <-> s. s -> w_2. ~s. Can we infer w_2 from them?
 From w_2 <-> s we can infer w_2 -> s. From w_2 -> s, s -> w_2 we can infer w_2 <-> s. Finally, from w_2 <-> s, ~s we can infer ~w_2, which contradicts w_2. Therefore, the answer is no.