Consider the following premises. p_6 -> q_6. q_6 -> s. s -> r. p_2 -> p_6. Can we infer p_2 -> r from them? If possible, name the inference rules being used at each step.
 From p_6 -> q_6, q_6 -> s we can infer p_6 -> s via transitivity. From p_2 -> p_6, p_6 -> s we can infer p_2 -> s via transitivity. Finally, from p_2 -> s, s -> r we can infer p_2 -> r via transitivity. Therefore, the answer is yes.