Class 12 NCERT • Mathematics Part 1 (New Syllabus)
Mathematics Part 1 Ch 01: Relations and Functions
Select a topic or study module below to explore types of relations (reflexive, symmetric, transitive, equivalence), types of functions (one-one, onto, bijective), composition of functions, invertible functions, binary operations, and comprehensive textbook problem solutions.
Topic 01 • Types of Relations
Exploring Empty, Universal, Reflexive, Symmetric, and Transitive Relations on Sets with Illustrative Examples
Topic 02 • Equivalence Relations
Analyzing Equivalence Relations, Partition of Sets, Equivalence Classes, and Geometric/Algebraic Proof Problems
Topic 03 • Injective & Surjective Functions
Studying Mapping Definitions, One-One (Injective), Many-One, Onto (Surjective), Into Functions, and Graphical Tests
Topic 04 • Bijective Functions
Investigating Bijective (One-One and Onto) Functions, Adjusting Domains and Codomains for Function Invertibility
Topic 05 • Composition of Functions
Examining Composite Mappings (g o f and f o g), Associativity Properties, and Solving Composite Equation Problems
Topic 06 • Invertible Functions
Analyzing Left and Right Inverses, Conditions for Invertibility, and Step-by-Step Inverse Function Calculations
Topic 07 • Binary Operations
Studying Definition of Binary Operations, Commutativity, Associativity, Identity Elements, and Inverse Elements
Module 08 • Solutions & Chapter Review