NCERT Solutions Class 11 Mathematics Chapter 1 Sets Download In Pdf

Chapter 1 Sets download in pdf

**Question 1. **Which of the following are sets ? Justify your asnwer.

(i) The collection of all the months of a year beginning with the letter J.

(ii) The collection of ten most talented writers of India.

(iii) A team of eleven best-cricket batsmen of the world.

(iv) The collection of all boys in your class.

(v) The collection of all natural numbers less than 100.

(vi) A collection of novels written by the writer Munshi Prem Chand.

(vii) The collection of all even integers.

(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.

**Question 2. **Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or in the blank
spaces:

(i) 5. . .A

(ii) 8 . . . A

(iii) 0. . .A

(iv) 4. . . A

(v) 2. . .A

(vi) 10. . .A

**Question 3. **Write the following sets in roster form:

(i) A = {x : x is an integer and –3 < x < 7}

(ii) B = {x : x is a natural number less than 6}

(iii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}

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

(
v) E = The set of all letters in the word

(vi) F = The set of all letters in the word

**Question 4. **Write the following sets in the set-builder form :

(i) (3, 6, 9, 12}

(ii) {2,4,8,16,32}

(iii) {5, 25, 125, 625}

(iv) {2, 4, 6, . . .} (v) {1,4,9, . . .,100}

**Question 5. **List all the elements of the following sets :

(i) A = {x : x is an odd natural number}
(ii) B = {x : x is an integer,
1
2
– < x
9
2 }

(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 }.

**
Question 6. **Match each of the set on the left in the roster form with the same set on the right
described in set-builder form:

(i) {1, 2, 3, 6} (a) {x : x is a prime number and a divisor of 6}

(ii) {2, 3} (b) {x : x is an odd natural number less than 10}

(iii) {M,A,T,H,E,I,C,S} (c) {x : x is natural number and divisor of 6}

(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}.

EXERCISE 1.2

**Question 1. **1Which of the following are examples of the null se

t
(i) Set of odd natural numbers divisible by 2

(ii) Set of even prime numbers

(iii) { x : x is a natural numbers, x < 5 and x > 7 }

(iv) { y : y is a point common to any two parallel lines}

**Question 2. **Which of the following sets are finite or infinite

(i) The set of months of a year

(ii) {1, 2, 3, . . .}

(iii) {1, 2, 3, . . .99, 100}

(iv) The set of positive integers greater than 100

(v) The set of prime numbers less than 99

**Question 3. **State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis

(ii) The set of letters in the English alphabet

(iii) The set of numbers which are multiple of 5

(iv) The set of animals living on the earth

(v) The set of circles passing through the origin (0,0)

**Question 4. **In the following, state whether A = B or not:

(i) A = { a, b, c, d } B = { d, c, b, a }

(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}

(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10}

(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }

**Question 4. **Are the following pair of sets equal ? Give reasons.

(i) A = {2, 3}, B = {x : x is solution of x2 + 5x + 6 = 0}

(ii) A = { x : x is a letter in the word FOLLOW}
B = { y : y is a letter in the word WOLF}

**Question 5. **From the sets given below, select equal sets :
A = { 2, 4, 8, 12}, B = { 1, 2, 3, 4}, C = { 4, 8, 12, 14}, D = { 3, 1, 4, 2}
E = {–1, 1}, F = { 0, a}, G = {1, –1}, H = { 0, 1}

EXERCISE 1.3

**Question 6. **Make correct statements by filling in the symbols ⊂ or in the blank spaces :

(i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 }

(ii) { a, b, c } . . . { b, c, d }

(iii) {x : x is a student of Class XI of your school}. . .{x : x student of your school}

(iv) {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with
radius 1 unit}

(v) {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}

(vi) {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane}
(

vii) {x : x is an even natural number} . . . {x : x is an integer}

**Question 2. ** Examine whether the following statements are true or false:

(i) { a, b } { b, c, a }

(ii) { a, e } ⊂ { x : x is a vowel in the English alphabe
t}

(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 }

(iv) { a }⊂ { a, b, c }

(v) { a }∈ { a, b, c }

(vi) { x : x is an even natural number less than 6} ⊂ { x : x is a natural number
which divides 36}

**Question 3. ** Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

(i) {3, 4} ⊂ A

(ii) {3, 4} ∈ A

(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A

(v) 1 ⊂ A

(vi) {1, 2, 5} ⊂ A

(vii) {1, 2, 5} ∈ A

(viii) {1, 2, 3} ⊂ A

(ix) φ ∈ A

(x) φ ⊂ A

(xi) {φ} ⊂ A

**Question 5. **Write down all the subsets of the following sets

(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) φ

**Question 6.** How many elements has P(A), if A = φ?
6. Write the following as intervals :

(i) {x : x ∈ R, – 4 < x ≤ 6}

(ii) {x : x ∈ R, – 12 < x < –10}

(iii) {x : x ∈ R, 0 ≤ x < 7} (iv) {x : x ∈ R, 3 ≤ x ≤ 4}

**Question 7. ** Write the following intervals in set-builder form :

(i) (– 3, 0)

(ii) [6 , 12]

(iii) (6, 12] (iv) [–23, 5)

**Question 8. ** What universal set(s) would you propose for each of the following :

(i) The set of right triangles.

(ii) The set of isosceles triangles.

**Question 9. ** Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the
following may be considered as universal set (s) for all the three sets A, B and C

(i) {0, 1, 2, 3, 4, 5, 6}

(ii) φ

(iii) {0,1,2,3,4,5,6,7,8,9,10}

(iv) {1,2,3,4,5,6,7,8}

**Question 1. **Find the union of each of the following pairs of sets :

(i) X = {1, 3, 5} Y = {1, 2, 3}

(ii) A = [ a, e, i, o, u} B = {a, b, c}

(iii) A = {x : x is a natural number and multiple of 3}
B = {x : x is a natural number less than 6}

(iv) A = {x : x is a natural number and 1 < x ≤ 6 }
B = {x : x is a natural number and 6 < x < 10 }

(v) A = {1, 2, 3}, B = φ

**Question 2. **Let A = { a, b }, B = {a, b, c}. Is A ⊂ B ? What is A ∪ B ?

**Question 3. ** If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

**Question 4. **If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8 }and D = { 7, 8, 9, 10 }; find (i) A ∪ B

(ii) A ∪ C

(iii) B ∪ C (iv) B ∪ D
(v) A ∪ B ∪ C (vi) A ∪ B ∪ D (vii) B ∪ C ∪ D

**Question 5. **Find the intersection of each pair of sets of question 1 above.

**Question 6. **If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15}and D = {15, 17}; find

(i) A ∩ B

(ii) B ∩ C

(iii) A ∩ C ∩ D

(iv) A ∩ C

(v) B ∩ D (vi) A ∩ (B ∪ C)

(vii) A ∩ D

(viii) A ∩ (B ∪ D)

(ix) ( A ∩ B ) ∩ ( B ∪ C )
(x) ( A ∪ D) ∩ ( B ∪ C)

**Question 7. **If A = {x : x is a natural number }, B = {x : x is an even natural number}
C = {x : x is an odd natural number}andD = {x : x is a prime number }, find

(i) A ∩ B

(ii) A ∩ C

(iii) A ∩ D
(iv) B ∩ C (v) B ∩ D (vi) C ∩ D

**Question 8. ** Which of the following pairs of sets are disjoint

(i) {1, 2, 3, 4} and {x : x is a natural number and 4 ≤ x ≤ 6 }

(ii) { a, e, i, o, u } and { c, d, e, f }

(iii) {x : x is an even integer } and {x : x is an odd integer}

**Question 9. ** If A = {3, 6, 9, 12, 15, 18, 21}, B = { 4, 8, 12, 16, 20 },
C = { 2, 4, 6, 8, 10, 12, 14, 16 }, D = {5, 10, 15, 20 }; find

(i) A – B

(ii) A – C

(iii) A – D

(iv) B – A

(v) C – A

(vi) D – A

(vii) B – C

(viii) B – D

(ix) C – B

(x) D – B

(xi) C – D

(xii) D – C

**Question 10. **If X= { a, b, c, d } and Y = { f, b, d, g}, find

(i) X – Y

(ii) Y –
X

(iii) X ∩ Y

**Question 11. ** If R is the set of real numbers and Q is the set of rational numbers, then what is
R – Q?

**Question 12. **State whether each of the following statement is true or false. Justify your answer.

(i) { 2, 3, 4, 5 } and { 3, 6} are disjoint sets.

(ii) { a, e, i, o, u } and { a, b, c, d }are disjoint sets.

(iii) { 2, 6, 10, 14 } and { 3, 7, 11, 15} are disjoint sets.

(iv) { 2, 6, 10 } and { 3, 7, 11} are disjoint sets.

**Question 1. **Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and
C = { 3, 4, 5, 6 }. Find

(i) A′

(ii) B′

(iii) (A ∪ C)′

(iv) (A ∪ B)′

(v) (A′)′

(vi) (B – C)′

**Question 2. ** If U = { a, b, c, d, e, f, g, h}, find the complements of the following sets :

(i) A = {a, b, c}

(ii) B = {d, e, f, g}

(iii) C = {a, c, e, g} (iv) D = { f, g, h, a}

**Question 3. ** Taking the set of natural numbers as the universal set, write down the complements
of the following sets:
(i) {x : x is an even natural number}

(ii) { x : x is an odd natural number }

(iii) {x : x is a positive multiple of 3}

(iv) { x : x is a prime number }

(v) {x : x is a natural number divisible by 3 and 5}

(vi) { x : x is a perfect square }

(vii) { x : x is a perfect cube}

(viii) { x : x + 5 = 8 }

(ix) { x : 2x + 5 = 9}
(x) { x : x ≥ 7 }

(xi) { x : x ∈ N and 2x + 1 > 10 }

**Question 4. **If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that

(i) (A ∪ B)′ = A′ ∩ B′

(ii) (A ∩ B)′ = A′ ∪ B′

**Question 5. **Draw appropriate Venn diagram for each of the following :

(i) (A ∪ B)′

(ii) A′ ∩ B′

(iii) (A ∩ B)′,

(iv) A′ ∪ B′

**Question 6. ** Let U be the set of all triangles in a plane. If A is the set of all triangles with at
least one angle different from 60°, what is A′?

**Question 7. **Fill in the blanks to make each of the following a true statement :

(i) A ∪ A′ = . . .

(ii) φ′ ∩ A = . . .

(iii) A ∩ A′ = . . .

(iv) U′ ∩ A = . . .

**Question 1. **If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n ( X ∪ Y ) = 38,
find n ( X ∩ Y ).

**Question 2. ** If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and
Y has 15 elements ; how many elements does X ∩ Y have?

**Question 3. **In a group of 400 people, 250 can speak Hindi and 200 can speak English. How
many people can speak both Hindi and English?

**Question 4. ** If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T
has 11 elements, how many elements does S ∪ T have?

**Question 5. **If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and
X ∩ Y has 10 elements, how many elements does Y have?

**Question 6. **In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least
one of the two drinks. How many people like both coffee and tea?

**Question 7. **In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many
like tennis only and not cricket? How many like tennis?

**Question 8. ** In a committee, 50 people speak French, 20 speak Spanish and 10 speak both
Spanish and French. How many speak at least one of these two languages?

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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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