Subset - Imported Knowlpedia Content

A subset of a set $B$ is a set $A$ such that every element of $A$ is an element of $B$ :

A\subseteq B \;\;:\!\iff\;\; \forall x\,(x\in A \Rightarrow x\in B).

Remarks

The subset relation is a basic way to compare sets and is used to define operations like power set and set difference. Note that $A=B$ holds exactly when both $A\subseteq B$ and $B\subseteq A$ .

Examples

$\{1,2\}\subseteq \{1,2,3\}$ .
For any set $A$ , $\varnothing\subseteq A$ (see empty set).