1. The problem here is to understand the basics of set theory and its fundamental concepts. 2. A set is a collection of distinct objects, called elements. For example, $A = \{1, 2, 3\}$ is a set containing elements 1, 2, and 3. 3. The main operations in set theory include: - Union: $A \cup B$ is the set of elements in $A$ or $B$. - Intersection: $A \cap B$ is the set of elements in both $A$ and $B$. - Difference: $A - B$ is the set of elements in $A$ but not in $B$. - Complement: $A^c$ is the set of elements not in $A$ relative to a universal set. 4. Another important concept is subsets: $A \subseteq B$ means every element of $A$ is also in $B$. 5. To understand deeper, consider Venn diagrams which visually represent these operations. 6. Example: If $A = \{1, 2, 3\}$ and $B = \{3, 4, 5\}$, then - $A \cup B = \{1, 2, 3, 4, 5\}$ - $A \cap B = \{3\}$ - $A - B = \{1, 2\}$ 7. Set theory forms the foundation for many areas in mathematics, computer science, and logic, making it essential to master these fundamental concepts.