Class 12 Mathematics — Chapter 1: RELATIONS AND FUNCTIONS

Chapter 1: RELATIONS AND FUNCTIONS is a chapter in Class 12 Mathematics (Part 1), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 6 topics including Empty and Universal Relations, Reflexive Relations, Symmetric Relations. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.

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What you'll learn

▸Empty and Universal Relations

empty relationuniversal relationtrivial relationssubset of A x Aphi
▸Reflexive RelationsCore concept

reflexivereflexivity(a, a)related to itselfidentity pair
▸Symmetric RelationsCore concept

symmetricsymmetryif (a,b) then (b,a)reciprocaltwo-way
▸Transitive RelationsCore concept

transitivetransitivitychain of relation(a,c)flow of relation
▸Equivalence RelationsCore concept

equivalence relationreflexivesymmetrictransitiveRST
▸Equivalence Classes and Partitions

equivalence classpartitiondisjoint subsets[a]subdivision

Chapter Summary

Understand the definitions of the two trivial relations: the empty relation (where no elements are related) and the universal relation (where every element is related to every other element). These represent the smallest and largest possible relations on a set.

Understand and test for the property of reflexivity in a relation. A relation R on a set A is reflexive if every element in A is related to itself, i.e., (a, a) ∈ R for every a ∈ A.

Understand and test for the property of symmetry in a relation. A relation R is symmetric if for any pair (a, b) in R, the pair (b, a) is also in R. It represents a two-way relationship.

Understand and test for the property of transitivity in a relation. A relation R is transitive if a relation between a and b, and b and c, implies a relation between a and c, i.e., if (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.

Define and identify an equivalence relation as a relation that is simultaneously reflexive, symmetric, and transitive. Students must be able to prove or disprove that a given relation is an equivalence relation by verifying all three properties.

Understand that an equivalence relation on a set partitions the set into mutually disjoint subsets, known as equivalence classes. Students should be able to determine the equivalence class for a given element.

Practice Questions from this Chapter

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Explain functions using everyday examples. Get Solution →
Show types of relations with drawings. Get Solution →
Give a non-math example of symmetry. Get Solution →
According to the text, what is the mathematical definition of a relation R from a set A to a set B? Get Solution →
A relation R in a set A is called an empty relation if which condition is met? Get Solution →
What is a universal relation R in a set A? Get Solution →
According to Definition 3, a relation R in a set A is reflexive if... Get Solution →
A relation R in a set A is called symmetric if which of the following is true? Get Solution →

Did you know?

💡 The equals sign (=) was invented in 1557 to avoid writing "is equal to".
💡 Ancient Romans did not have a symbol for zero in their number system.
💡 Infinity can be "countable" or "uncountable," meaning some infinities are larger.
💡 There are more irrational numbers than rational numbers, even though both are infinite.
💡 A googol is a number with one followed by one hundred zeros.

Frequently Asked Questions

How many topics are covered in this chapter?

This chapter covers 6 key topics: Empty and Universal Relations, Reflexive Relations, Symmetric Relations, Transitive Relations, Equivalence Relations, and more. The BrainWeave AI tutor explains each one with examples.

Is Chapter 1: RELATIONS AND FUNCTIONS important for board exams?

Yes — Class 12 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.

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Related Chapters

Chapter 2: INVERSE TRIGONOMETRIC FUNCTIONS

Chapter 3: MATRICES

Chapter 4: Determinants

Chapter 7: PROOFS IN MATHEMATICS

Chapter 8: Mathematical Modelling

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