Final answer:
Methods such as isEmpty() and size() do not require the bag invariant to be part of their implicit precondition because they do not alter the bag's structure. Conversely, methods that modify the content, like add() or remove(), usually rely on the bag invariant to ensure proper functioning.
Step-by-step explanation:
When discussing bags in the context of data structures and algorithms, the term 'bag invariant' typically refers to a property or set of properties that must hold true for the bag to maintain its intended structure and function correctly. Methods associated with a bag's operation can have preconditions, which are assumptions or requirements that must be met before the method can be correctly executed.
The bag methods that often do not require the bag invariant as part of their implicit precondition include methods that check whether the bag is empty or ascertain the number of elements in the bag, such as isEmpty() or size(). These methods do not manipulate the structure of the bag and therefore do not depend on the bag being in a particular state.
On the other hand, methods that add or remove items, such as add() or remove(), generally require the bag invariant to be upheld as a part of their implicit precondition to ensure that the methods perform as expected and that the bag's integrity is maintained.