What is the Difference Between Subset and Superset?
🆚 Go to Comparative Table 🆚The difference between a subset and a superset lies in the relationship between two sets and their elements.
A subset of a set A is any set B such that every element of B is also an element of A. In other words, a subset contains only some of the elements of the original set. For example, if A = {1, 2, 3, 4}, then B = {2, 4} is a subset of A because all elements in B are also in A.
A strict subset is a subset that is not equal to the original set, meaning B must have at least one fewer element than A.
A superset of A is any set C such that A is a subset of C. In other words, a superset contains all the elements of the original set and possibly additional elements. For example, if A = {1, 2, 3, 4}, then C = {1, 2, 3, 4, 5} is a superset of A because A is a subset of C and C contains an additional element (5) that is not in A.
In summary:
- A subset contains only some of the elements of the original set.
- A superset contains all the elements of the original set and possibly additional elements.
- A strict subset is a subset with at least one fewer element than the original set.
Comparative Table: Subset vs Superset
The difference between a subset and a superset can be understood through the following table:
| Subset | Superset |
|---|---|
| A subset is a set whose elements are all contained within another set. | A superset is a set that contains all the elements of another set, as well as possibly additional elements. |
| A subset does not contain elements outside of those in the superset. | A superset includes the subset's elements and potentially more. |
| Symbolically, a subset is represented as A ⊆ B or A ⊂ B, where A is the subset and B is the superset. | Symbolically, a superset is represented as B ⊇ A or B ⊃ A, where B is the superset and A is the subset. |
For example, consider two sets: Set A = {1, 2, 3} and Set B = {1, 2, 3, 4, 5}. In this case, Set A is a subset of Set B because all the elements of Set A (1, 2, and 3) are also present in Set B. On the other hand, Set B is a superset of Set A because it contains all the elements of Set A and additional elements (4 and 5).
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