Class 11 Mathematics — Chapter 2: RELATIONS AND FUNCTIONS

Chapter 2: RELATIONS AND FUNCTIONS is a chapter in Class 11 Mathematics (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 8 topics including Ordered Pairs and Cartesian Product (A × B), Equality of Ordered Pairs, Cardinality of Cartesian Products (n(A × B)). 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

▸Ordered Pairs and Cartesian Product (A × B)Core concept

Cartesian productordered pairA × Bnon-empty sets
▸Equality of Ordered PairsCore concept

equal ordered pairscorresponding elementssolve for x and yequality
▸Cardinality of Cartesian Products (n(A × B))

number of elementsn(A × B)cardinalitypq elements
▸Ordered Triplets and Geometric Interpretation

ordered tripletA × A × AR × RR × R × Rthree-dimensional space
▸Definition of a RelationCore concept

relationsubsetA × Brelationship
▸Domain, Codomain, and Range of a RelationCore concept

domainrangecodomainimage
▸Representation of Relations

roster formset-builder formarrow diagramvisual representation
▸Total Number of Relations

total relationsnumber of relations2^(pq)number of subsets

Chapter Summary

Understand the concept of an ordered pair and how to form the Cartesian product of two non-empty sets, P × Q, which is the set of all possible ordered pairs (p, q) where p is from P and q is from Q.

Understand that two ordered pairs (a, b) and (c, d) are equal if and only if their corresponding elements are equal (a = c and b = d). This is used to solve equations for unknown variables.

Know the formula for the number of elements in a Cartesian product: if set A has 'p' elements and set B has 'q' elements, then the set A × B has 'pq' elements.

Understand the extension of Cartesian products to three sets (A × A × A) to form ordered triplets. Recognize that R × R geometrically represents the 2D coordinate plane and R × R × R represents 3D space.

Understand that a relation R from a set A to a set B is a subset of the Cartesian product A × B. The elements in the relation are ordered pairs that satisfy a specific defined condition.

Define and identify the domain (set of all first elements), range (set of all second elements, or images), and codomain (the entire second set B) for a given relation. Understand that the range is always a subset of the codomain.

Learn to represent a relation in different forms: Roster form (listing the ordered pairs), Set-builder form (describing the rule), and using an Arrow Diagram for visual representation.

Understand that the total number of possible relations from a set A (with p elements) to a set B (with q elements) is 2^(pq), as this is the number of possible subsets of A × B.

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

Illustrate Cartesian product visually. Get Solution →
Explain ordered pairs' uses. Get Solution →
Describe different types of sets. Get Solution →
What is the Cartesian product P × Q of two non-empty sets P and Q? Get Solution →
If set A has p elements and set B has q elements, how many elements will the Cartesian product A × B have? Get Solution →
An ordered pair (a, b, c) where a, b, c belong to the same set A is called what? Get Solution →
When are two ordered pairs (a, b) and (c, d) considered equal? Get Solution →
What is a relation R from a non-empty set A to a non-empty set B? Get Solution →

Did you know?

💡 The mathematical concept of 'sets' was introduced by Georg Cantor in the late 19th century.
💡 An empty set contains no elements, yet it is a fundamental concept in mathematics.
💡 Ordered pairs are essential for describing locations in video games and computer graphics.
💡 Rene Descartes invented the Cartesian coordinate system, which uses ordered pairs.
💡 There are infinitely many points on a line, each represented by an ordered value.

Frequently Asked Questions

How many topics are covered in this chapter?

This chapter covers 8 key topics: Ordered Pairs and Cartesian Product (A × B), Equality of Ordered Pairs, Cardinality of Cartesian Products (n(A × B)), Ordered Triplets and Geometric Interpretation, Definition of a Relation, and more. The BrainWeave AI tutor explains each one with examples.

Is Chapter 2: RELATIONS AND FUNCTIONS important for board exams?

Class 11 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.

Can I get NCERT solutions for this chapter in Hindi?

Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.

Is BrainWeave free for Class 11 - Science?

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Related Chapters

Chapter 1: SETS

Chapter 3: TRIGONOMETRIC FUNCTIONS

Chapter 13: STATISTICS

Chapter 14: PROBABILITY

Chapter 9: STRAIGHT LINES

Chapter 10: CONIC SECTIONS

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