Consider the following premises. q_2 <-> q_8. t -> q_8. u or t. u -> q_2. Can we infer ~q_8 from them? If possible, name the inference rules being used at each step.
 From q_2 <-> q_8 we can infer q_2 -> q_8 via biconditional elimination. From u -> q_2, q_2 -> q_8 we can infer u -> q_8 via transitivity. Finally, from u -> q_8, t -> q_8, u or t we can infer q_8 via disjunction elimination, which contradicts ~q_8. Therefore, the answer is no.