Question about areas where no gun signs hold force of law

I live in Ohio, which allows private business owners to put up no gun signs. These hold the force of law, but is that only if you are asked to leave? I know there's certain areas where it's completely illegal to carry, but how do private businesses work? Am I breaking the law if I enter one, or am I only breaking the law if I enter, get asked to leave, and don't? via /r/CCW https://ift.tt/2K3Cr5w