Jun 21, 2024

- Teacher: Shivani Sharma
- Class 12, CBSE Board
- For both Hindi and English Medium

**Key Concepts:**Set, Cartesian Product, Relation**Important Point:**Knowledge of sets and Cartesian products is necessary to understand relations

**Definition:**A well-defined collection of objects**Example:**Set of natural numbers < 10 (1, 3, 5, 7, 9)**Symbol:**Sets are represented by capital letters

**Definition:**The set of all possible ordered pairs**Example:**Set A = {1, 3, 5}, Set B = {2, 4}. Then A × B = {(1,2), (1,4), (3,2), (3,4), (5,2), (5,4)}

**Definition:**Relation from A to B is a subset of A × B**Example:**Relation R, where the first element must be smaller than the second**Types:**Reflexive, Symmetric, Transitive**Explained with examples**

**Definition:**Every element must be related to itself (a, a) ∈ R**Example:**Set {1, 2, 3} is reflexive if (1,1), (2,2), (3,3) are all in R

**Symmetric:**If (a, b) ∈ R, then (b, a) must also be in R**Transitive:**If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R**Example:**Set {1, 2, 3} is symmetric and transitive if it follows these conditions

**Definition:**Must be reflexive, symmetric, and transitive**Example:**Set {1, 2, 3} is an equivalence relation if it fulfills all three conditions

**Definition:**Partitioning a set based on an equivalence relation**Example:**Set {0, 1, 2, ..., 12}, divided based on multiples of mod 4

- In the next video, we will solve problems from Exercise 1.1
- Advise everyone to study hard and pay attention