Skip to main content
Super TutorResources
Chapter 1 of 13
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Chapter Summary

Relations and Functions

ICSE · Class 12 · Mathematics

Summary of Relations and Functions for ICSE Class 12 Mathematics. Key concepts, important points, and chapter overview.

104 questions28 flashcards5 concepts

Interactive on Super Tutor

Studying Relations and Functions? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for chapter summary and more.

Try Super Tutor — Free

1,000+ Class 12 students started this chapter today

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.
Super Tutor

This is just one of 5+ visuals inside Super Tutor's Relations and Functions chapter

Explore the full set

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 Comprehensive Overview of Relations and Functions Chapter, Shows how Cartesian Product creates all ordered pairs from two sets, Arrow diagram showing a relation from set A to set B with multiple connections. These are the concepts ICSE Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Relations and Functions — ICSE Class 12 Mathematics?
Understand the core concepts first, then work through the 104 practice questions available for this chapter. Revise formulas and 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.

More resources for Relations and Functions

All 13 chapters — ICSE Class 12 Mathematics Chapter Summary

For serious students

Get the full Relations and Functions chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for ICSE Class 12 Mathematics.

Try Super Tutor Free
Try the full chapter — Free