Consider the following premises. p_4 or q. u -> p_4. q -> u. u <-> p_4. Can we infer u from them? If possible, name the inference rules being used at each step.
 From u <-> p_4 we can infer p_4 -> u via biconditional elimination. From u -> p_4, p_4 -> u we can infer u <-> p_4 via biconditional introduction. From u <-> p_4 we can infer p_4 -> u via biconditional elimination. Finally, from p_4 -> u, q -> u, p_4 or q we can infer u via disjunction elimination. Therefore, the answer is yes.