Consider the following premises. p_9. s_4 <-> q. p_9 -> q. s_4 <-> u. Can we infer ~s_4 from them? If possible, name the inference rules being used at each step.
 From s_4 <-> q we can infer q -> s_4 via biconditional elimination. From p_9 -> q, q -> s_4 we can infer p_9 -> s_4 via transitivity. From s_4 <-> u we can infer u -> s_4 via biconditional elimination. From p_9 we can infer p_9 or u via addition. Finally, from p_9 -> s_4, u -> s_4, p_9 or u we can infer s_4 via disjunction elimination, which contradicts ~s_4. Therefore, the answer is no.