Mathematics chapters
  1. 013D Geometry
  2. 02Application of Derivatives
  3. 03Area Under Curves
  4. 04Binomial Theorem
  5. 05Circles
  6. 06Complex Numbers
  7. 07Continuity & Differentiability
  8. 08Definite Integration
  9. 09Determinants
  10. 10Differential Equations
  11. 11Ellipse
  12. 12Hyperbola
  13. 13Indefinite Integration
  14. 14Inequalities & Modulus
  15. 15Inverse Trigonometric Functions
  16. 16Limits
  17. 17Logarithms
  18. 18Matrices
  19. 19Methods of Differentiation
  20. 20Number System & Basics
  21. 21Parabola
  22. 22Permutations & Combinations
  23. 23Probability
  24. 24Properties of Triangle
  25. 25Quadratic Equations
  26. 26Sequences & Series
  27. 27Sets, Relations & Functions
  28. 28Statistics
  29. 29Straight Lines
  30. 30Trigonometric Equations
  31. 31Trigonometric Ratios & Identities
  32. 32Vectors

Chapter 27 · Class 11-12 & JEE Main/Adv

Sets, Relations & Functions

60 topics in 13 parts

Full lessonClass 11 Mathematics · Relations and Functions
Types of Sets Subsets & Power Sets Universal Set Cartesian Product Union & Intersection Set Difference

Key ideas

+Y +Z +X O(0,0,0) Line L A(x₁, y₁, z₁) a P(x, y, z) r Parallel Vector b = aî + bĵ + ck̂ Cartesian Form: (x - x₁)/a = (y - y₁)/b = (z - z₁)/c = λ ⟺ General Point: (x₁ + λa, y₁ + λb, z₁ + λc)
Sets, Relations & Functions

Analytical Comparison & Distinction Matrix

Analytical MethodStandard RepresentationParametric / Invariant Framework
Algebraic NatureExplicit equations relating spatial coordinatesParameterized using scalar parameters (λ, μ) or vectors
Symmetry UsageRelies on coordinate expansionExploits vector dot/cross products for rapid simplification
Computational EfficiencyDirect for intercept evaluationSuperior for angles, orthogonal projections, and distances
Common MistakeSign confusion in determinantsOmitting boundary condition checks

All 60 topics in Sets, Relations & Functions

  1. Sets & Their Representations

    • Set Representation
    • Types of Sets
    • Equal Sets
    • Subsets
    • Intervals as Subsets of R
    • Power Set
    • Universal Set
    • Set Cardinality
    • Cartesian Product

  2. Operations on Sets

    • Union of Sets
    • Intersection of Sets
    • Difference of Sets
    • Complement of a Set
    • Venn Diagrams
    • Inclusion-Exclusion & Practical Problems

  3. Relations

    • Definition, Domain, Range & Inverse
    • Reflexive Relations
    • Symmetric Relations
    • Transitive Relations
    • Equivalence Relations & Equivalence Classes
    • Counting Relations

  4. Number System & Inequalities

    • Number System
    • Intervals & Sign Scheme
    • Algebraic & Modulus Inequalities
    • Common Inequalities

  5. Function

    • Definition & Vertical Line Test
    • Domain
    • Co-Domain & Range
    • Function as a Set of Ordered Pairs
    • Monotonicity
    • Equality of Functions

  6. Different Types of Functions

    • Algebraic Function
    • Polynomial Function
    • Rational Function
    • Exponential & Logarithmic Functions
    • Trigonometric Functions
    • Inverse Trigonometric Functions
    • Modulus Function
    • Signum Function
    • Greatest Integer & Fractional Part Functions
    • Piecewise & Max-Min Functions
    • Bounded Function
    • Homogeneous Function
    • Implicit & Explicit Functions

  7. Different Types of Mappings (Functions)

    • One-One & Many-One Functions
    • Onto & Into Functions
    • Number of Functions (Mappings)

  8. Even & Odd Functions

    • Even Function
    • Odd Function
    • Extension of Domain

  9. Periodic Functions

    • Finding Period
    • Graphs & Range of Periodic Functions

  10. Composite Function

    • Composition of Functions
    • Properties of Composite Functions

  11. Inverse Functions

    • Existence of Inverse Functions
    • Properties of Inverse Functions

  12. Transformation of Graphs

    • Translation, Scaling & Reflection
    • Graphs of Standard Functions

  13. Functional Equation

    • Equations Resulting from Properties of Functions
    • Equations Satisfied by Typical Functions