Subset: a set contained in a set

Two weeks ago, we have talked about the basics of sets.  In this post, we are going to talk about subsets.


If you understand what this means, then you have a notion of a subset.

In mathematics, if A and B are sets, we say that A is a subset of B, denoted by A \subseteq B, if all elements of A are also elements of B. The easiest way to illustrate this is through a Venn diagram as shown on the right.  In the Venn diagram, set A is within set B. Therefore, all elements of set A are also elements of B.

Example 1

LetB be set of all letters in the English alphabet and A be the set of vowel letters. It is clear that A \subseteq B since {aeiou} are elements A and also are elements of B. » Read more