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Relations and Functions — Revision Notes

ICSE · Class 12 · Mathematics

Relations and Functions revision notes for ICSE Class 12 Mathematics: 4 topics in quick points. Part of the ICSE Class 12 Mathematics syllabus.

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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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 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 Revision Notes

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