# Relations And Functions class 11 Notes Mathematics

## myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

CBSE Mathematics Chapter 2 Relations And Functions class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Relations And Functions class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on Chapter 2 Relations And Functions class 11 Notes Mathematics are also available for download in CBSE Guide website.

## CBSE Guide Relations And Functions class 11 Notes

CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.

## Relations And Functions class 11 Notes Mathematics

Download CBSE class 11th revision notes for Chapter 2 Relations And Functions class 11 Notes Mathematics in PDF format for free. Download revision notes for Relations And Functions class 11 Notes Mathematics and score high in exams. These are the Relations And Functions class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

CBSE Class 11 Mathematics
Revision Notes
Chapter – 2
Relations And Functions class 11 Notes Mathematics

1. Cartesian Product of Sets
2. Relations
3. Functions
•  Ordered pair  A pair of elements grouped together in a particular order. Clearly, $\left( {a,b} \right) \ne \left( {b,a} \right)$.
• Cartesian product of two sets A and B is given by A × B =  {(a, b): a ∈ A, b ∈ B}.

In particular R × R = {(x, y): x, y ∈ R} and R × R × R = (x, y, z): x, y, z ∈ R}

• If (a, b) = (x, y), then a =  x and b = y.
•  If n(A) = p and  n(B) =  q, then n(A × B) = pq.
• A × φ = φ
•  In general, A × B ≠ B × A.
•  Relation: Relation A relation R from a set A to a set B is a subset of the Cartesian product A × B obtained by describing a relationship between the first element x and the second element y of the ordered pairs in A × B, i.e., ${\rm{R}} \subseteq {\rm{A}} \times {\rm{B}}$.
• Number of Relations: Let A and B be two non-empty finite sets, comtaining m and n elements respectively, then the total number of relaitons from A to B is ${2^{mn}}$
• Domain: The domain of R is the set of all first elements of the ordered pairs in a relation R. Domain R = $\left\{ {a:\left( {a,b} \right) \in {\rm{R}}} \right\}$.
• The image of an element x under a relation R is given by y, where (x, y) ∈ R,
• Range: The range of the relation R is the set of all second elements of the ordered pairs in a relation R. Range R = $\left\{ {b:\left( {a,b} \right) \in {\rm{R}}} \right\}$.
• Function: Function A function f  from a set A to a set B is a specific type of relation for which every element x of set A has one and only one image y in set B. We write  f: A→B, where f(x) =  y.
• Domain and Co-domain: The set A is called the domain of function f and the set B is called the co-domain of f.
• Range: If f is a function from A to B, then each element of A corresponds to ine and only one element of B, whereas every element in B need not be the image of some $x$ in A. The subset of B comtaining the image of elements of A is called the range of the function. The range of f is denoted by $f\left( {\rm{A}} \right)$. Mathematically, we write: $f\left( {\rm{A}} \right) = \left\{ {f\left( x \right):x \in {\rm{A}}} \right\}$
• Image: If the element x of A corresponds to $y \in {\rm{B}}$ under the function f, then we say that $y$ is the image of $x$ under f and we write, $f\left( x \right) = y$.
• Pre-image: If $f\left( x \right) = y$, then $x$ is pre-image of $y.$