Consider the following premises. p_3 <-> p_4. p_8 <-> p_4. p_3 or p_8. Can we infer ~p_4 from them? If possible, name the inference rules being used at each step.
 From p_8 <-> p_4 we can infer p_8 -> p_4 via biconditional elimination. From p_3 <-> p_4 we can infer p_3 -> p_4 via biconditional elimination. Finally, from p_3 -> p_4, p_8 -> p_4, p_3 or p_8 we can infer p_4 via disjunction elimination, which contradicts ~p_4. Therefore, the answer is no.