1. Let's start by understanding what a set is. A set is a collection of distinct objects, considered as an object in its own right. 2. For example, the set of natural numbers less than 5 is written as $A = \{1, 2, 3, 4\}$. 3. Sets can be described by listing their elements or by a property that defines them, e.g., $B = \{x : x \text{ is an even number less than } 10\} = \{2, 4, 6, 8\}$. 4. Important operations on sets include union ($A \cup B$), intersection ($A \cap B$), and difference ($A - B$). 5. The union of two sets $A$ and $B$ is the set of elements that are in $A$ or $B$ or both. 6. The intersection of two sets $A$ and $B$ is the set of elements that are common to both $A$ and $B$. 7. The difference $A - B$ is the set of elements that are in $A$ but not in $B$. 8. For example, if $A = \{1, 2, 3\}$ and $B = \{2, 3, 4\}$, then: - $A \cup B = \{1, 2, 3, 4\}$ - $A \cap B = \{2, 3\}$ - $A - B = \{1\}$ 9. Sets can also be subsets of each other. $A$ is a subset of $B$ if every element of $A$ is also in $B$, denoted $A \subseteq B$. 10. The empty set $\emptyset$ is a set with no elements and is a subset of every set. This covers the basics of sets for class 11 CBSE.