CBSE · Senior secondary

CBSE Class 12 — Notes, Chapters & Practice Quizzes

Master every Class 12 chapter — the base your board marks and your NEET / JEE / CUET prep both stand on.

13 subjects 166 chapters 171 practice quizzes NCERT syllabus
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Class 12 Mathematics — Chapter-wise Notes & Quizzes

Mathematics · 13 chapters
Summary, key terms, important questions and a practice quiz with AI diagnosis for each.

Chapter 1: Relations and Functions

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A relation that is reflexive, symmetric and transitive is called:

Summary

This chapter deepens the study of relations and functions begun in Class 11. A relation on a set is examined for the properties of being reflexive, symmetric and transitive; a relation that is all three is called an equivalence relation, and it partitions the set into disjoint equivalence classes. The chapter then classifies functions as one-one (injective), onto (surjective) and bijective. A function \(f:A\to B\) is one-one if \(f(x_1)=f(x_2)\Rightarrow x_1=x_2\), and onto if every element of \(B\) is the image of some element of \(A\). Composition of functions \((g\circ f)(x)=g(f(x))\) is introduced, and a bijection is shown to have an inverse \(f^{-1}\) satisfying \(f^{-1}\circ f=I\). These ideas form the backbone for inverse trigonometric functions and for understanding invertibility throughout calculus and algebra.

Types of relationsEquivalence relations and classesOne-one, onto and bijective functionsComposition of functionsInvertible functions

Key terms

Equivalence relation
A relation that is reflexive, symmetric and transitive.
One-one (injective)
Distinct inputs give distinct outputs: \(f(x_1)=f(x_2)\Rightarrow x_1=x_2\).
Onto (surjective)
Every element of the codomain is an image of some element of the domain.
Bijective
A function that is both one-one and onto.
Composition
\((g\circ f)(x)=g(f(x))\), applying \(f\) then \(g\).
Invertible function
A bijection \(f\) for which \(f^{-1}\) exists with \(f^{-1}\circ f=I\).

Important questions

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Equivalence relation
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A relation that is reflexive, symmetric and transitive.
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Practice quiz · Relations and Functions

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Relations and Functions

Maths 10 Qs · ~10 min