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Relations and Functions — Concept Maps

Punjab Board · Class 12 · Mathematics

2 concept maps of Relations and Functions for Punjab Board Class 12 Mathematics, each also written out as a text outline.

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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2 Concept Maps

Complete Overview of Relations and Functions Concepts

Complete Overview of Relations and Functions Concepts

The map in words

  • Relations and Functions
    • Relations
      • Definition
        • Subset of A × B
        • Connects elements
      • Types of Relations
        • Reflexive
          • aRa for all a
        • Symmetric
          • aRb implies bRa
        • Transitive
          • aRb and bRc implies aRc
        • Equivalence
          • Has all three
          • Creates partitions
      • Properties
        • Empty relation
        • Universal relation
        • Equivalence classes
    • Functions
      • Definition
        • f: X → Y
        • Each input one output
      • Properties
        • Domain
        • Codomain
        • Range
      • Classifications
        • One-One
          • Different inputs
          • Different outputs
        • Onto
          • Every codomain
          • Has preimage
        • Bijective
          • Both injective
          • and surjective
      • Operations
        • Composition gof
        • Not commutative
        • Associative
      • Invertibility
        • f inverse exists
        • Only if bijective
        • fof^-1 = I

Decision tree showing classification of relations as empty, universal, or partial

Decision tree showing classification of relations as empty, universal, or partial

The map in words

  • Relation R in Set A
    • Is R Empty?
      • YES: Empty Relation R = φ No pairs exist
        • Trivial Relation
      • NO: Is R = A × A?
        • YES: Universal Relation R = A × A All pairs exist
        • NO: Partial Relation Some pairs exist

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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.
What do the concept maps for Relations and Functions show?
The 2 maps show how the ideas in Relations and Functions connect: Complete Overview of Relations and Functions Concepts; Decision tree showing classification of relations as empty, universal, or partial. Each map is also written out as an outline on this page.
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.

More resources for Relations and Functions

All Punjab Board Class 12 Mathematics Concept Maps

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