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Relations and Functions — Chapter Summary

Madhya Pradesh Board · Class 12 · Mathematics

Summary of Relations and Functions for Madhya Pradesh Board Class 12 Mathematics. Part of the Madhya Pradesh Board Class 12 Mathematics syllabus.

119 questions52 flashcards15 formulas & key relations5 concepts

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A visual representation of the Cartesian product A × B using a grid or mapping diagram, showing how ordered pairs are formed.
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Overview

Relations are subsets of a Cartesian product, and functions are special relations with a precise rule of association. The chapter develops the basic language of domain, codomain, range, types of relations, equivalence relations, types of functions, composition, and invertibility. It also shows how t

Key Concepts

A relation in a set

A relation in a set A is a subset of A × A. For two sets A and B, a relation from A to B is any subset of A × B. If (a, b) belongs to the relation, th

The empty relation contains no ordered

The empty relation contains no ordered pair. The universal relation contains every ordered pair in A × A. These are also called trivial relations.

A relation is reflexive if every

A relation is reflexive if every element is related to itself, symmetric if related pairs can be reversed, and transitive if the relation passes throu

A relation is an equivalence relation

A relation is an equivalence relation if it is reflexive, symmetric, and transitive. Examples include congruence of triangles and the relation on inte

An equivalence relation divides a set

An equivalence relation divides a set into mutually disjoint equivalence classes whose union is the whole set. For integers under modulo 2, the classe

Learning Objectives

  • Understand the meaning of a relation as a subset of A × A or A × B.
  • Identify empty, universal, reflexive, symmetric, transitive, and equivalence relations.
  • Recognize equivalence classes and partitions formed by equivalence relations.
  • Classify functions as one-one, many-one, onto, or bijective.
  • Use composition of functions correctly and see that composition is not commutative in general.

Frequently Asked Questions

What are the important topics in Relations and Functions for Madhya Pradesh Board Class 12 Mathematics?
Key topics in Relations and Functions include Relations and Their Types, Functions: One-One, Onto, and Bijective, Composition of Functions and Inverse, Historical Development of Function. Study these first, then practise questions on each for the Madhya Pradesh Board Class 12 board exam.
How should I revise Relations and Functions for the Madhya Pradesh Board Class 12 board exam?
Learn the core ideas first, then work through the 119 practice questions on Relations and Functions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Relations and Functions

All Madhya Pradesh Board Class 12 Mathematics Chapter Summary

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