No person having the possession of a dog shall lead or take such dog upon the private property of another without permission, or knowingly permit any such dog to soil on, damage or destroy the yards, flowers or shrubbery of another person, or otherwise trespass upon the property of another without permission. No person having the possession of a cat shall knowingly permit any such cat to soil on, damage or destroy yards, flowers or shrubbery of another person or otherwise damage the property of another. For purposes of this section, "knowingly" means that the person having possession of a dog or cat has been made aware, by previous incidents, of its propensity to destroy or damage the property of another, and has failed to take action which will prohibit the same.