Consider the following premises. r_2 -> p_2. q_1 or ~p_2. p_2 <-> q_1. Can we infer ~(r_2 -> q_1) from them?
 From p_2 <-> q_1 we can infer q_1 -> p_2. From q_1 or ~p_2 we can infer p_2 -> q_1. From q_1 -> p_2, p_2 -> q_1 we can infer q_1 <-> p_2. From q_1 <-> p_2 we can infer p_2 -> q_1. Finally, from r_2 -> p_2, p_2 -> q_1 we can infer r_2 -> q_1, which contradicts ~(r_2 -> q_1). Therefore, the answer is no.