1. The problem is to explain the set rules used in mathematics. 2. Sets are collections of distinct objects, considered as an object in their own right. 3. Key rules include membership: an element either belongs to a set or not, denoted $x \in A$ or $x \notin A$. 4. Common operations on sets: - Union ($A \cup B$): all elements in $A$, $B$, or both. - Intersection ($A \cap B$): elements common to both $A$ and $B$. - Difference ($A \setminus B$): elements in $A$ but not in $B$. - Complement ($A^c$): elements not in $A$ (relative to a universal set). 5. Set equality: two sets $A$ and $B$ are equal if every element of $A$ is in $B$ and vice versa, written $A = B$. 6. Special sets: empty set ($\emptyset$) has no elements; universal set contains all elements under consideration. 7. Subsets: $A$ is a subset of $B$ ($A \subseteq B$) if every element of $A$ is also in $B$. 8. Power set: the set of all subsets of a set $A$, denoted $\mathcal{P}(A)$. These rules govern how sets behave and interact, forming a foundation for many areas of mathematics.