Given a set E, a subset of E is the set in which all of the elements belong to set E.
- Synonym for part of a set.
- A proper or strict subset of a set E is a subset of E that is not equal to E.
- A large subset of a set E is a subset of E that includes only a part of E or the entirety of set E.
Symbols
- To indicate that set A is a proper or strict subset of set E, we write: A ⊂ E.
- To indicate that set A is a large subset of set E, we write: A ⊆ E.
- To indicate a subset of E that does not contain any elements (called an empty subset), we use the symbol ∅.
- In this diagram, set E is a strict subset of U.
Example
Consider set E = {0, 2, 4, 6, 8, 10} and set A = {2, 4, 8}.
Set A is a subset of set E because all of the elements in set A belong to set E and we write: A ⊂ E.