Subset

Let $A$ and $B$ be sets . We say that $A$ is a subset of $B$, written $A \subseteq B$, if

The subset relation is a basic way to compare sets; it also underlies the partial order $\subseteq$ on collections of subsets.

Examples:

• $\{1,2\} \subseteq \{1,2,3\}$.
• $\emptyset \subseteq A$ for every set $A$.
• $A \subseteq A$ for every set $A$.
• $\{1,2,3\} \nsubseteq \{1,2\}$ since $3 \in \{1,2,3\}$ but $3 \notin \{1,2\}$.