Consider the following premises. p_2 -> p. p_2 -> u. ~p. u -> p_2. Can we infer u from them? If possible, name the inference rules being used at each step.
 From u -> p_2, p_2 -> u we can infer u <-> p_2 via biconditional introduction. From p_2 -> p, ~p we can infer ~p_2 via modus tollens. Finally, from u <-> p_2, ~p_2 we can infer ~u via biconditional elimination, which contradicts u. Therefore, the answer is no.