Consider the following premises. s_2 and q_10. q_1 -> u. s_2 -> q_1. Can we infer ~u from them? If possible, name the inference rules being used at each step.
 From s_2 and q_10 we can infer s_2 via simplification. From s_2 -> q_1, q_1 -> u we can infer s_2 -> u via transitivity. Finally, from s_2 -> u, s_2 we can infer u via modus ponens, which contradicts ~u. Therefore, the answer is no.