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Relations and Functions - I

NIOS · Class 12 · Mathematics

Complete topic list for Relations and Functions - I in NIOS Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

44 questions25 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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4 Topics · NIOS Class 12 Mathematics

Topics in Relations and Functions - I

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

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 Relations and Functions - Complete Concept Overview, Relations and Functions: Concept Hierarchy, Mind map showing the hierarchical structure of all major topics in Relations and Functions chapter. These are the concepts NIOS Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Relations and Functions - I — NIOS Class 12 Mathematics?
Understand the core concepts first, then work through the 44 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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