Consider the following premises. u or ~s. q_2 <-> s. u -> w. ~w. Can we infer ~q_2 from them?
 From u -> w, ~w we can infer ~u. From u or ~s we can infer s -> u. From s -> u, ~u we can infer ~s. Finally, from q_2 <-> s, ~s we can infer ~q_2. Therefore, the answer is yes.