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.

sets-and-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

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