Proper Subsets

$A$ is a proper subset of $B$ if and only if every element in $A$ is also contained in $B$ and $B$ contains at least one element that is not in $A$.

For example, $\{1,2\}$ is a subset of $\{1,2\}$ but it is not a proper subset.

The notation for proper subset is $A\subset B$. Some authors may also use $A⊊B$.