Vocabulary - Subset

Set $A$ is a subset of set $B$ if every element of $A$ is also in $B$. You write $A \subseteq B$.

For example, $\{1, 2\} \subseteq \{1, 2, 3\}$ because $1$ and $2$ are both in $\{1, 2, 3\}$. But $\{1, 4\} \not\subseteq \{1, 2, 3\}$ because $4$ is not in the second set.

Every set is a subset of itself: $A \subseteq A$. Also, the empty set $\emptyset$ is a subset of every set.