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Relations and Functions Overview
Jun 21, 2024
Math Class Teaching Notes: Relations and Functions
Introduction
Teacher: Shivani Sharma
Class 12, CBSE Board
For both Hindi and English Medium
Chapter: Relations and Functions
Chapter 1.1: Introduction and Overview
Key Concepts:
Set, Cartesian Product, Relation
Important Point:
Knowledge of sets and Cartesian products is necessary to understand relations
Sets
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
Cartesian Product
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)}
Relations
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
Reflexive Relation
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 and Transitive Relation
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
Equivalence Relation
Definition:
Must be reflexive, symmetric, and transitive
Example:
Set {1, 2, 3} is an equivalence relation if it fulfills all three conditions
Equivalence Classes
Definition:
Partitioning a set based on an equivalence relation
Example:
Set {0, 1, 2, ..., 12}, divided based on multiples of mod 4
Conclusion
In the next video, we will solve problems from Exercise 1.1
Advise everyone to study hard and pay attention
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Full transcript