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Relations and Functions - I — Revision Notes

NIOS · Class 12 · Mathematics

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

44 questions25 flashcards2 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

2.1 Cartesian Product of Two Sets

  • Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B
  • Notation: A × B = {(a, b) : a ∈ A and b ∈ B}
  • Order matters: A × B ≠ B × A (unless A = B or one is empty)
2

2.2 Relations: Definition, Domain, Range, and Codomain

  • A relation R from set A to set B is any subset of A × B
  • Notation: R ⊆ A × B or R = {(a, b) : a ∈ A, b ∈ B and aRb}
  • Domain of R: set of all first elements of ordered pairs in R
3

2.3 Functions: Definition, Types, and Properties

  • A function f: A → B is a special relation where each element of A has EXACTLY ONE image in B
  • Key condition: No two ordered pairs can have the same first element
  • Every element of domain must have an image (unlike relations)
4

2.3.2 Finding Domain and Range of Functions

  • Domain must exclude values making denominator zero in rational functions
  • Domain must exclude values making expression under square root negative
  • For y = 1/f(x), domain excludes where f(x) = 0

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Full Notes

Key Concepts

The Cartesian product of two setsA relation R from setDomainA function is a special typeA graphical method to determine if

Frequently Asked Questions

What are the important topics in Relations and Functions - I for NIOS Class 12 Mathematics?
Key topics in Relations and Functions - I include 1 Cartesian Product of Two Sets, 2 Relations: Definition, Domain, Range, and Codomain, 3 Functions: Definition, Types, and Properties, 3.2 Finding Domain and Range of Functions. Study these first, then practise questions on each for the NIOS Class 12 board exam.
How should I revise Relations and Functions - I for the NIOS Class 12 board exam?
Learn the core ideas first, then work through the 44 practice questions on Relations and Functions - I. 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 NIOS Class 12 Mathematics Revision Notes

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