Consider the following premises. w_2 or q. p_1 <-> p_2. w_2 -> p_1. q -> p_1. ~p_2. Can we infer q_1 from them? If possible, name the inference rules being used at each step.
 From p_1 <-> p_2, ~p_2 we can infer ~p_1 via biconditional elimination. From w_2 -> p_1, q -> p_1, w_2 or q we can infer p_1 via disjunction elimination. From p_1 we can infer p_1 or q_1 via addition. Finally, from p_1 or q_1, ~p_1 we can infer q_1 via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.