1. Let's start by understanding what set theory is. Set theory is a branch of mathematical logic that studies sets, which are collections of objects. 2. A set is usually denoted by capital letters like $A$, $B$, $C$, and its elements are listed within curly braces, for example, $A = \{1, 2, 3\}$. 3. Important operations in set theory include union ($A \cup B$), intersection ($A \cap B$), difference ($A - B$), and complement ($A^c$). 4. The union of two sets $A$ and $B$ is the set of elements that are in $A$, or in $B$, or in both. 5. The intersection of two sets $A$ and $B$ is the set of elements that are in both $A$ and $B$. 6. The difference $A - B$ is the set of elements that are in $A$ but not in $B$. 7. The complement $A^c$ is the set of all elements not in $A$, relative to a universal set $U$. 8. Let's consider an example: If $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$, then $$A \cup B = \{1, 2, 3, 4\}$$ $$A \cap B = \{2, 3\}$$ $$A - B = \{1\}$$ $$B - A = \{4\}$$ 9. These operations help us analyze and understand relationships between different groups of objects. 10. Understanding these basics will prepare you for more advanced topics in set theory such as subsets, power sets, and Cartesian products.