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Relations and Functions — Revision Notes

Tamil Nadu Board · Class 10 · Mathematics

Relations and Functions revision notes for Tamil Nadu Board Class 10 Mathematics: 4 topics in quick points. Includes Ordered Pairs and Cartesian Product.

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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Key Topics to Revise

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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.
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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.
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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'.
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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.

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Full Notes

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 Ordered Pairs and Cartesian Product, Relations, Functions – Definition and Basic Concepts, Types of Functions. Study these first, then practise questions on each for the Tamil Nadu Board Class 10 board exam.
How should I revise Relations and Functions for the Tamil Nadu Board Class 10 board exam?
Learn the core ideas first, then work through the 45 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 Tamil Nadu Board Class 10 Mathematics Revision Notes

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