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