NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1

In NCERT Solutions for class 11 Maths Chapter 1 Sets, you will learn about the description of a Set, types of sets, subsets, concepts of subsets, Venn Diagrams, Operations on Sets using Venn Diagrams, Laws of Algebra of sets, some important results on number of elements in sets.

Free download NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1, Ex 1.2, Ex 1.3, Ex 1.4, Ex 1.5, Ex 1.6 and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus.

Topics and Subtopics in Class 11 Maths NCERT Solutions Chapter 1 Sets

Section Name	Topic Name
1	Sets
1.1	Introduction
1.2	Sets and their Representations
1.3	The Empty Set
1.4	Finite and Infinite Sets
1.5	Subsets
1.6	Power Set
1.7	Universal Set
1.8	Venn Diagrams
1.9	Operations on Sets
1.10	Complement of a Set
1.11	Practical Problems on Union and Intersection of Two Sets
1.12	Summary

Class 11 Maths NCERT Solutions Chapter 1 Sets Ex 1.1

Ex 1.1 Class 11 Maths Q.1: Which of the following are sets. Explain your answer.
(a).  The collection of all day in a week which have the first letter S.
(b).  The collection of ten most famous singers of India.
(c).  A group of best football strikers of the world.
(d).  The collection of all girls in your school.
(e).  The collection of all odd numbers below 50.
(f).  A collection of poems written by the poet Shakespeare.
(g).  The collection of all prime numbers.
(h).  The collection of questions in science book.
(i).  A collection of most dangerous reptiles in India.

Solution:
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identity a month that belongs to this collection. Hence, this collection is a set.
(ii) The collection of ten most talented writer of India is not a well-defined collection because the criteria for determining a writer’s talent vary from person to person. Hence, this collection is not a set.
(iii) A team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsman’s talent may vary from person to person. Hence, this collection is not a set.
(iv) The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection. Hence, this collection is a set.
(v) The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection. Hence, this collection is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because one can definitely identify a book that belongs to this collection. Hence, this collection is a set.
(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection.
Hence, this collection is a set.
(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter. Hence, this collection is a set.
(ix) The collection of most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person. Hence, this collection is not a set.

Ex 1.1 Class 11 Maths Q.2: Let P = {2, 3, 4, 5, 6, 7}. Insert the correct symbol ∈or∉ inside the given blank spaces below:
(a).  2 . . . . . . . . . . P
(b).  9 . . . . . . . . . P
(c).  11 . . . . . . . . P
(d).  4 . . . . . . . . P
(e).  0 . . . . . . . . P
(f).  7 . . . . . . . . P

Solution:
(i) 5 ∈ A
(ii) 8 ∉ A
(iii) 0 ∉ A
(iv) 4 ∈ A
(v) 2 ∈ A
(vi) 10 ∉ A

Ex 1.1 Class 11 Maths Q.3: Write the given sets in roster form:
(a).  P = {y: y is an integer and -4 < y < 6}.
(b).  Q = {y: y is a natural number which is <8}
(c).  R = {y: y is a 2 digit natural number in which the sum of its digits is 9}
(d).  S = {y: y is a prime number which is a divisor of 70}
(e).  T = The set of all letters in the word ELEPHANT
(f).  U = The set of all letters in the word DIVISION

Solution:
(i) A = {x: x is an integer and –3 < x < 7}
The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.
Therefore, the given set can be written in roster form as
A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {x: x is a natural number less than 6}
The elements of this set are 1, 2, 3, 4, and 5 only.
Therefore, the given set can be written in roster form as
B = {1, 2, 3, 4, 5}

(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only.
Therefore, this set can be written in roster form as
C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv) D = {x: x is a prime number which is a divisor of 60}

2	60
2	30
3	15
	5

∴60 = 2 × 2 × 3 × 5
The elements of this set are 2, 3, and 5 only.
Therefore, this set can be written in roster form as D = {2, 3, 5}.

Ex 1.1 Class 11 Maths Q.4: Write the given sets in set-builder form:
(a).  {4, 8, 12, 16, 20}
(b).  {3, 9, 27, 81}
(c).  {4, 16, 64, 256, 1024}
(d).  {1, 3, 5, 7…}
(e).  {1, 8, 27, 64….1000}

Solution:

Ex 1.1 Class 11 Maths Q.5: List all the elements of the following sets :
(i) A = {x : x is an odd natural number}

(iii) C = {x : x is an integer, x2 < 4}
(iv) D = {x : x is a letter in the word “LOYAL”}
(v) E = {x : x is a month of a year not having 31 days}
(vi) F = {x : x is a consonant in the English alphabet which precedes k}.

Solution:

Ex 1.1 Class 11 Maths Q.6: Match the following:

(A)	{1, 2, 3, 6}	(i)	{y: y is a divisor of 6 and also a prime number}
(B)	{T, R, I, G, O, N, M, E, Y}	(ii)	{y: y is less than 10 and also an odd number}
(C)	{2, 3}	(iii)	{y: y is natural number divisor of 6}
(D)	{1, 3, 5, 7, 9}	(iv)	{y: y is a letter of the word TRIGONOMETRY}

Solution: