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