Consider the following premises. q_2 or q_4. ~s. w_2 or ~q_4. q_2 -> s. s -> q_2. Can we infer ~w_2 from them?
 From s -> q_2, q_2 -> s we can infer s <-> q_2. From w_2 or ~q_4 we can infer q_4 -> w_2. From s <-> q_2, ~s we can infer ~q_2. From q_2 or q_4, ~q_2 we can infer q_4. Finally, from q_4 -> w_2, q_4 we can infer w_2, which contradicts ~w_2. Therefore, the answer is no.