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Relations and Functions

ICSE · Class 12 · Mathematics

Quick revision notes for Relations and Functions — ICSE Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

104 questions28 flashcards5 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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Key Topics to Revise

1

1. Cartesian Product and Relation

  • The Cartesian product of two sets forms ordered pairs.
  • A relation from A to B is any subset of A × B.
  • A relation on a set A is a subset of A × A.
2

2. Domain, Co-domain, Range, and Inverse Relation

  • Domain is the set of all first components of ordered pairs in a relation.
  • Range is the set of all second components of ordered pairs in a relation.
  • Co-domain is the target set B for a relation from A to B.
3

3. Standard Relations on a Set

  • Empty relation means no element is related to any element.
  • Universal relation means every element is related to every element.
  • Identity relation relates each element only to itself.
4

4. Reflexive, Symmetric, and Transitive Relations

  • A relation is reflexive if every element is related to itself.
  • A relation is symmetric if related pairs can be reversed.
  • A relation is transitive if chained pairs produce the direct pair.

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Full Notes

Key Concepts

For two sets A and BA relation from A to BThe domain of a relationIf R is a relation fromA relation on A is

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.

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All 13 chapters — ICSE Class 12 Mathematics Revision Notes

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