In Hohfeld's jural relations, liberty and duty are jural opposites, not correlatives. Liberty (privilege) is the opposite of duty - if you have a liberty to do something, no one has a right that you should not do it. Duty is the opposite - you are legally required to act or refrain from acting. They cancel each other out - where liberty exists, duty cannot exist, and vice versa. This differs from right-duty pairs which are correlatives (your right implies another's duty).