1. The problem is to understand what a subset is in mathematics. 2. A subset is a set where every element in it is also an element of another set. 3. The formal definition: If $A$ and $B$ are sets, then $A$ is a subset of $B$ if every element of $A$ is also in $B$. This is written as $A \subseteq B$. 4. Important rule: The empty set $\emptyset$ is a subset of every set. 5. Example: If $B = \{1, 2, 3\}$, then $A = \{1, 2\}$ is a subset of $B$ because all elements of $A$ are in $B$. 6. Another example: $C = \{4\}$ is not a subset of $B$ because $4$ is not in $B$. 7. Summary: A subset contains only elements from the original set, possibly all or none (empty set).