Subset
Pronunciation: /ˈsʌbˌsɛt/ Explain
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

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
 Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 1/24/2010. Buy the book
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 3. Thomson, Brooks/Cole. 2005. Buy the book
More Information
 McAdams, David E. Sets. Life is a Story Problem LLC. 4/3/2009. http://www.lifeisastoryproblem.com/algebra/sets.html.
Cite this article as:
McAdams, David E. Subset. 5/5/2011. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/subset.html.
Image Credits
Revision History
6/7/2008: Corrected spelling. (
McAdams, David E.)
3/28/2008: Added proper subset. (
McAdams, David E.)
7/31/2007: Initial version. (
McAdams, David E.)