1.3.4.2 Improper Subset and Improper Superset

If all the elements of  are also elements of  and  does not contain any additional element, then  is an improper subset of , denoted by  ⊆ . Equivalently, we can also say that  is an improper superset of , denoted by  ⊇

Example 1.12. To illustrate this, consider set  = {1, 2, 3}, then its improper subset is the set itself, i.e:

• {1, 2, 3}