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