How does the Set data structure ensure the uniqueness of inserted elements?

The Set data structure ensures element uniqueness through hashing (in hash-sets) or ordered trees (in tree-based implementations). When adding an element, the following checks occur:

• The hash is computed or compared with existing elements.
• If the element already exists, insertion does not happen.
• If the element does not exist, it is added to the structure.

Thus, Set does not allow duplicates, guaranteeing that each element appears only once.

Example in Swift:

var numbers: Set<Int> = [1, 2, 3]
numbers.insert(2) // will not add, as 2 already exists
numbers.insert(4) // will add 4
print(numbers) // Outputs [1, 2, 3, 4]