Consider the following premises. p_10 -> q_10. r_10 -> q. q_10 -> r_10. p_10. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From p_10 -> q_10, q_10 -> r_10 we can infer p_10 -> r_10 via transitivity. From p_10 -> r_10, p_10 we can infer r_10 via modus ponens. Finally, from r_10 -> q, r_10 we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.