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CBSE Notes for Class 11 Mathematics chapter 1. Sets: Introduction, quick revision notes for Class 11 Mathematics chapter 1. Sets Introduction, Chapter-wise CBSE Revision Notes, CBSE Notes PDF Free Download, CBSE One Liner Notes Class 11, Half Yearly Revision Notes, CBSE Revision Notes Class 11 Mathematics
Get CBSE Notes for Class 11 Mathematics Chapter 1. Sets: Introduction prepared by experts as per the latest NCERT syllabus and CBSE exam pattern. These concise and easy-to-understand notes cover important definitions, formulas, diagrams, and key concepts from the chapter to help students in quick revision and effective exam preparation. Whether you are studying for school tests, board exams, or competitive exams, these notes provide a reliable study resource. Designed in simple language with point-wise explanations, they save time and enhance learning efficiency. Download free PDF notes, explore solved examples, and strengthen your understanding of [Topic Name] for scoring high marks. Perfect for Class 11 students who want clear, structured, and exam-oriented notes for CBSE Mathematics.
SETS
Set: A collection of well defined objects is called a set.
- Objects of collection is called "element" or "member".
Properties:
(i) All elements of a set should have special property.
(ii) They all should be differ to each other or they do not repeat.
(iii) They should be well defined.
A, B, C, D ........................ X, Y, Z
Example : A = {a, b, c, d} Or B = {1, 2, 3, 4}
Standard symbols of some special sets:
N : the set of all natural numbers
Z : the set of all integers
Q : the set of all rational numbers
R : the set of real numbers
Z+ : the set of positive integers
Q+ : the set of positive rational numbers, and
R+ : the set of positive real numbers.
Symbols and their meaning:
(i) " ∈ " (epsilon) : "belong to"
If a is an element of a set A, we say that “ a belongs to A”
in symbolic form we write it as : a ∈ A
(ii) " ∉ " : "not belong to"
When any element which not belong to any given set then we use symbol ∉ : "not belong to"
if a is not an element of set A. we say that "a not belong to A"
in symbolic form we write it as : a ∉ A
(iii) " ⇒ " : emplies
In common language "⇒" means "emply toward ..... also ......"
(iv) " = " : Equal to
A = B, it means set A is equal to set B.
(v) " ≠ " : Not equal to
A ≠ B, It means set A not equal to set B.
(vi) “⇔” is a symbol for two way implications, and is usually read as " if and only if ".
(vii) " : " : colon Here in the set colon stands for "such that"
Representation of sets:
Every set is introduced by its elements. So for expressing a set before we have to express its elements.
Now, Method to express the elements of a set.
(1) Roster Or tabular form :
In roster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces { }. For example,
(i) First five natural numbers:
A = {1, 2, 3, 4, 5}.
(ii) First four letter of English Alphabets
B = {a, b, c, d}.
(iii) The set of all natural numbers which divide 42
C = {1, 2, 3, 6, 7, 14, 21, 42}.
(iv) The set of all vowels in the English alphabet.
D = {a, e, i, o, u}.
Note:
In Roster Form no-element is generally repeated
Example:
The set of letters forming the word 'ELEMENT'
E = {E, L, M, N, T}
Here no-element has been repeated.
(2) Set-builder form
In set-bulder form, all the elements of a set possess a single common property
which is not possessed by any element outside the set.
Example:
D = { a, e, i, o, u}
All elements of set A have a common property e.i vowel in English alphabet.
Then, in set-builder form:
D = { x : x is a vowel in english alphabet }
This set will be read as :
" the set of all x such that x is a vowel in english alphabet. "
C = {y : y is a natural number which divides 42}
B = (z : z is a first four letter of english alphabet}
Other examples
(i) A = {1, 2, 9, 25} Roster form
Set-builder form
A = {x : x = n2, where n ∈ N and n < 6}
(ii) B = {P, R, I, N, C, A, L}
Set-builder form
B = {x : x is a letter of the word PRINCIPAL}
(iii) C = {1, 2, 3, 6, 9, 18}
Set-builder form
C = { x : x is a positive integer and is a divisor of 18}
(iv) D = (3, 6, 9, 12}
Set-builder form
D = {x : x = 3n where n ∈ N and 0 < n < 5}
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