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.