Subset

Subset

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.

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