Consider the following premises. s or r. s <-> q_2. q. r -> q_2. Can we infer ~q_2 from them? If possible, name the inference rules being used at each step.
 From s <-> q_2 we can infer s -> q_2 via biconditional elimination. Finally, from s -> q_2, r -> q_2, s or r we can infer q_2 via disjunction elimination, which contradicts ~q_2. Therefore, the answer is no.