The sin inherited from Adam will ultimately produce acts of sin in our lives. None of us can claim to have never told a lie. If we do deny it, we are guilty of committing the very sin we deny. In Romans 3 Paul continues his indictment of mankind by accusing him of being totally without righteousness. To support his accusation, Paul makes a second conclusion.
Most people believe the law was given as a way to become righteous.
They believe that by keeping the law they can attain righteousness. In reality the law was given to prove to man that he cannot be righteous through his own efforts. And it shall be our righteousness, if we observe to do all these commandments before the LORD our God, as he hath commanded us. The law only made a man righteous if he observed to do all of its commandments. Every broken law of God stands as proof of man's sinfulness.