Consider the following premises. s_3 -> q_2. s_3 or r. r -> q_2. q_2 -> s_3. Can we infer ~q_2 from them? If possible, name the inference rules being used at each step.
 From q_2 -> s_3, s_3 -> q_2 we can infer q_2 <-> s_3 via biconditional introduction. From q_2 <-> s_3 we can infer s_3 -> q_2 via biconditional elimination. Finally, from s_3 -> q_2, r -> q_2, s_3 or r we can infer q_2 via disjunction elimination, which contradicts ~q_2. Therefore, the answer is no.