Subset

Pronunciation: /ˈsʌbˌsɛt/ ?

If set A is a subset of set B, all members of set A are also members of set B. We write 'A ⊆ B'. We can also say that set B contains set A.

If A is a subset of set B and sets A and B are not equal to each other, set A is a proper subset of set B. We write 'A ⊂ B'.

Example 1

Set B is represented as a circle labeled B. Set A is represented as a circle labeled A. The circle representing A is entirely contained within the circle representing set B.
Figure 1: Set A is a subset of set B.

Example 2

Think of a bunch of sheep. All the sheep are animals. But, there are animals that are not sheep, such as dogs. So the set of sheep is a subset of the set of animals, but the set of animals is not a subset of the set of sheep. The set of animals contains animals that are not sheep.

Example 3

Since every integer is also a real number, the set of integers is a subset of the set of real numbers.

References

  1. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 3. Thomson, Brooks/Cole, 2005.

More Information

  • McAdams, David. Sets. Life is a Story Problem LLC. 2009-04-03. http://www.lifeisastoryproblem.org/algebra/sets.html.

Printed Resources

Cite this article as:


Subset. 2008-06-07. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/subset.html.

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2008-06-07: Corrected spelling (McAdams, David.)
2008-03-28: Added proper subset (McAdams, David.)
2007-07-31: Initial version (McAdams, David.)

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