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Relations and Functions — Chapter Summary

ICSE · Class 12 · Mathematics

Summary of Relations and Functions for ICSE Class 12 Mathematics. Key concepts: For two sets A and B, A relation from A to B and The domain of a relation.

104 questions28 flashcards16 formulas & key relations5 concepts

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A visual representation of a relation R from set A to set B as a subset of the Cartesian product A x B, showing elements of A mapped to elements of B.
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Overview

A relation connects two sets by pairing elements from one set with elements of another set. The Cartesian product A × B is the set of all ordered pairs (a, b) such that a belongs to A and b belongs to B. A relation from A to B is any subset of A × B, while a relation on A is a subset of A × A. The c

Key Concepts

For two sets A and B

For two sets A and B, the Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. If at least one of the sets is empty,

A relation from A to B

A relation from A to B is any subset R of A × B. If (a, b) ∈ R, then a is related to b by R. The number of relations from A to B is 2^(pq) when n(A) =

The domain of a relation

The domain of a relation is the set of all first components of its ordered pairs. The co-domain is the set B when the relation is from A to B. The ran

If R is a relation from

If R is a relation from A to B, then its inverse relation is R^-1 = {(b, a) : (a, b) ∈ R}. The domain of R is the range of R^-1, and the range of R is

A relation on A is

A relation on A is a relation from A to itself, so R ⊆ A × A. If n(A) = p, then the number of relations on A is 2^(p^2).

Learning Objectives

  • Understand Cartesian product and ordered pairs
  • Define a relation from one set to another and a relation on a set
  • Find domain, range, co-domain, and inverse of a relation
  • Recognize empty, universal, and identity relations
  • Test relations for reflexive, symmetric, and transitive properties

Frequently Asked Questions

What are the important topics in Relations and Functions for ICSE Class 12 Mathematics?
Key topics in Relations and Functions include Cartesian Product and Relation, Domain, Co-domain, Range, and Inverse Relation, Standard Relations on a Set, Reflexive, Symmetric, and Transitive Relations. Study these first, then practise questions on each for the ICSE Class 12 board exam.
How should I revise Relations and Functions for the ICSE Class 12 board exam?
Learn the core ideas first, then work through the 104 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 ICSE Class 12 Mathematics Chapter Summary

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