Proper Subset

Set $A$ is a proper subset of $B$ if $A \subseteq B$ and $A \neq B$. You write $A \subset B$.

For example, $\{1, 2\} \subset \{1, 2, 3\}$ is true, but $\{1, 2, 3\} \subset \{1, 2, 3\}$ is false because they are equal.

Proper subsets exclude the case where $A = B$. This distinction matters in proofs and problem constraints.