# 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 'AB'. 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 'AB'.

#### Example 1

 Figure 1: Set A is a subset of set B; A ⊂ 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. McAdams, David E.. All Math Words Dictionary, subset. 2nd Classroom edition 20150108-4799968. pg 172. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1, 1996. Buy the book
3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 3. Thomson, Brooks/Cole. 2005. Buy the book

• McAdams, David E.. Sets. Life is a Story Problem LLC. 4/3/2009. http://www.lifeisastoryproblem.com/algebra/sets.html.

McAdams, David E. Subset. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/subset.html.

### Revision History

5/7/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)