Skip to main content
Super TutorResources
Chapter 1 of 15
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Revision Notes

Relations and Functions

Madhya Pradesh Board · Class 12 · Mathematics

Quick revision notes for Relations and Functions — Madhya Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

119 questions52 flashcards5 concepts

Interactive on Super Tutor

Studying Relations and Functions? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

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

This is just one of 8+ visuals inside Super Tutor's Relations and Functions chapter

Explore the full set

Key Topics to Revise

1

1. Relations and Their Types

  • A relation in a set A is a subset of A × A.
  • The two extreme relations are the empty relation ϕ and the universal relation A × A.
  • Empty relation means no element of A is related to any element of A.
2

2. Functions: One-One, Onto, and Bijective

  • A function is a special relation with a well-defined image for each element of the domain.
  • One-one means distinct elements of the domain have distinct images.
  • Many-one means at least two different domain elements have the same image.
3

3. Composition of Functions and Inverse

  • Composition means applying one function after another.
  • The notation gof means g(f(x)).
  • Composition is generally not commutative: gof may differ from fog.
4

4. Historical Development of Function

  • Descartes first used the word function in 1637 in Geometrie to mean a positive integral power x^n of a variable x.
  • James Gregory considered a function as a quantity obtained from other quantities by algebraic or other operations.
  • Leibnitz used the word function for quantities varying along a curve and was the first to use the phrase function of x.

Get complete notes with diagrams and examples

Full Notes

Key Concepts

A relation in a setThe empty relation contains no orderedA relation is reflexive if everyA relation is an equivalence relationAn equivalence relation divides a set

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.

More resources for Relations and Functions

All 15 chapters — Madhya Pradesh Board Class 12 Mathematics Revision Notes

For serious students

Get the full Relations and Functions chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Madhya Pradesh Board Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free