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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.

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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?
Relations and Functions - I covers several key topics that are frequently asked in NIOS Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Relations and Functions - I — NIOS Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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