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Relations and Functions — Syllabus

Punjab Board · Class 12 · Mathematics

What Relations and Functions covers in Punjab Board Class 12 Mathematics: 4 topics, for the 2026-27 session. Topics include Types of Relations, Types.

45 questions25 flashcards4 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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4 Topics · Punjab Board Class 12 Mathematics · 2026-27

Topics in Relations and Functions

1

Types of Relations

  • A relation R in a set A is a subset of A × A (the Cartesian product of A with itself).
  • Empty Relation: R = φ (no element is related to any other element). Example: R = {(a,b): a – b = 10} in A = {1,2,3,4} is empty.
  • Universal Relation: R = A × A (every element is related to every element). Example: R = {(a,b): |a – b| ≥ 0} in A = {1,2,3,4} is universal.
2

Types of Functions

  • One-One (Injective) Function: Different inputs always give different outputs. f(x₁) = f(x₂) ⟹ x₁ = x₂.
  • Many-One Function: Two or more different inputs can give the same output. Example: f(x) = x² is many-one since f(1) = f(–1) = 1.
  • Onto (Surjective) Function: Every element of the co-domain Y is the image of at least one element in the domain X. Range of f = Y.
3

Composition of Functions

  • If f: A → B and g: B → C, then the composition gof: A → C is defined as gof(x) = g(f(x)) for all x ∈ A.
  • The composition 'gof' means 'first apply f, then apply g'. Read from right to left.
  • gof ≠ fog in general — composition is NOT commutative.
4

Invertible Functions

  • A function f: X → Y is invertible if there exists a function g: Y → X such that gof = Iₓ and fog = Iy.
  • g is called the inverse of f and is written as f⁻¹.
  • CRITICAL: A function is invertible if and only if it is BIJECTIVE (both one-one and onto).

Key Concepts

A relation R from setA relation R in setA relation R in setA relation R in setA relation R in set

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Frequently Asked Questions

What are the important topics in Relations and Functions for Punjab Board Class 12 Mathematics?
Key topics in Relations and Functions include Types of Relations, Types of Functions, Composition of Functions, Invertible Functions. Study these first, then practise questions on each for the Punjab Board Class 12 board exam.
How should I revise Relations and Functions for the Punjab Board Class 12 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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