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Chapter Summary

Relations and Functions

Madhya Pradesh Board · Class 12 · Mathematics

Summary of Relations and Functions for Madhya Pradesh Board Class 12 Mathematics. Key concepts, important points, and chapter overview.

119 questions52 flashcards5 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?
Relations and Functions covers several key topics that are frequently asked in Madhya Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Relations and Functions — Madhya Pradesh Board Class 12 Mathematics?
Understand the core concepts first, then work through the 119 practice questions available for this chapter. Revise formulas and 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.

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All 15 chapters — Madhya Pradesh Board Class 12 Mathematics Chapter Summary

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