Consider the following premises. u -> u_3. q. q -> u. u_3 -> p_2. Can we infer ~p_2 from them? If possible, name the inference rules being used at each step.
 From q -> u, u -> u_3 we can infer q -> u_3 via transitivity. From q -> u_3, u_3 -> p_2 we can infer q -> p_2 via transitivity. Finally, from q -> p_2, q we can infer p_2 via modus ponens, which contradicts ~p_2. Therefore, the answer is no.