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Relations and Functions — Revision Notes

Madhya Pradesh Board · Class 12 · Mathematics

Relations and Functions revision notes for Madhya Pradesh Board Class 12 Mathematics: 4 topics in quick points.

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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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.

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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?
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.

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All Madhya Pradesh Board Class 12 Mathematics Revision Notes

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