Subset

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

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 ).