How can we ensure the soundness and completeness of propositional logic?

To ensure the soundness and completeness of propositional logic, we must verify that all logical arguments are valid and that all valid conclusions can be reached using the rules of propositional logic. Soundness means that the premises of an argument logically lead to the conclusion, while completeness means that all valid conclusions can be derived from the premises. This can be achieved through rigorous proof methods and adherence to the rules of propositional logic.