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Relations and Functions

Tamil Nadu Board · Class 10 · Mathematics

Complete topic list for Relations and Functions in Tamil Nadu Board Class 10 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions24 flashcards5 concepts

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A diagram illustrating the domain, range, and co-domain of a relation R from set A to set B, highlighting which elements belong to each category.
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4 Topics · Tamil Nadu Board Class 10 Mathematics

Topics in Relations and Functions

1

1. Ordered Pairs and Cartesian Product

  • An ordered pair (a, b) is a pair of elements where ORDER MATTERS. So (2, 3) ≠ (3, 2).
  • Two ordered pairs (a, b) and (c, d) are equal ONLY IF a = c AND b = d.
  • The Cartesian Product A × B is the set of ALL possible ordered pairs (a, b) where a ∈ A and b ∈ B.
2

2. Relations

  • A relation R from A to B is any SUBSET of A × B.
  • If (x, y) ∈ R, we write xRy meaning 'x is related to y'.
  • Domain of R = set of all FIRST elements (from set A) that appear in R.
3

3. Functions – Definition and Basic Concepts

  • A function is a SPECIAL relation where EVERY element of the domain has EXACTLY ONE image.
  • Two conditions for a function: (1) Every element of X must have an image; (2) The image must be UNIQUE (one element cannot map to two different outputs).
  • A function f: X → Y is written as f(x) = y, meaning 'f maps x to y'.
4

4. Types of Functions

  • ONE-ONE (Injective): Different inputs → different outputs. f(a₁) = f(a₂) ⟹ a₁ = a₂.
  • MANY-ONE: Two or more elements of A have the SAME image in B. NOT a one-one function.
  • ONTO (Surjective): Range = Co-domain. Every element of B has at least one pre-image in A.

Key Concepts

An ordered pair consists of twoThe Cartesian product of two nonA relation R from setFor a relation R fromA function f from set

Frequently Asked Questions

What are the important topics in Relations and Functions for Tamil Nadu Board Class 10 Mathematics?
Key topics in Relations and Functions include Relations and Functions – Complete Chapter Overview, Relations and Functions – Complete Concept Map, Relations and Functions - Concept Overview. These are the concepts Tamil Nadu Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Relations and Functions — Tamil Nadu Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 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 8 chapters — Tamil Nadu Board Class 10 Mathematics Syllabus

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