(b) Yes, this statement is correct.  It is only when the law imposes a duty to avoid causing harm that liability for such harm arises in Negligence. Put another way, there is no liability for careless acts unless there is a recognised duty of care, even if the acts cause damage, and even if they are performed carelessly.

In Donoghue v Stevenson [1932] AC 562 Lord Macmillan said:

"....The law takes no cognisance of carelessness in the abstract. It concerns itself with carelessness only where there is a duty to take care and where failure in that duty has caused damage. In such circumstances carelessness assumes the legal quality of negligence and entails the consequences in law of negligence..."