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 β 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 β3 < 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
β < x
9
2 }

(iii) C = {x : x is an integer, x2 β€ 4}

(iv) D = {x : x is a letter in the word βLOYALβ}

(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 β€ 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 = {β1, 1}, F = { 0, a}, G = {1, β1}, H = { 0, 1}

EXERCISE 1.3

**Question 6. **Make correct statements by filling in the symbols β 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 } β { x : x is a vowel in the English alphabe
t}

(iii) { 1, 2, 3 } β { 1, 3, 5 }

(iv) { a }β { a, b, c }

(v) { a }β { a, b, c }

(vi) { x : x is an even natural number less than 6} β { 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} β A

(ii) {3, 4} β A

(iii) {{3, 4}} β A
(iv) 1 β A

(v) 1 β A

(vi) {1, 2, 5} β A

(vii) {1, 2, 5} β A

(viii) {1, 2, 3} β A

(ix) Ο β A

(x) Ο β A

(xi) {Ο} β A

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

(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) Ο

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

(i) {x : x β R, β 4 < x β€ 6}

(ii) {x : x β R, β 12 < x < β10}

(iii) {x : x β R, 0 β€ x < 7} (iv) {x : x β R, 3 β€ x β€ 4}

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

(i) (β 3, 0)

(ii) [6 , 12]

(iii) (6, 12] (iv) [β23, 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) Ο

(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 β€ 6 }
B = {x : x is a natural number and 6 < x < 10 }

(v) A = {1, 2, 3}, B = Ο

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

**Question 3. ** If A and B are two sets such that A β B, then what is A βͺ 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 βͺ B

(ii) A βͺ C

(iii) B βͺ C (iv) B βͺ D
(v) A βͺ B βͺ C (vi) A βͺ B βͺ D (vii) B βͺ C βͺ 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 β© B

(ii) B β© C

(iii) A β© C β© D

(iv) A β© C

(v) B β© D (vi) A β© (B βͺ C)

(vii) A β© D

(viii) A β© (B βͺ D)

(ix) ( A β© B ) β© ( B βͺ C )
(x) ( A βͺ D) β© ( B βͺ 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 β© B

(ii) A β© C

(iii) A β© D
(iv) B β© C (v) B β© D (vi) C β© 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 β€ x β€ 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 β B

(ii) A β C

(iii) A β D

(iv) B β A

(v) C β A

(vi) D β A

(vii) B β C

(viii) B β D

(ix) C β B

(x) D β B

(xi) C β D

(xii) D β C

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

(i) X β Y

(ii) Y β
X

(iii) X β© Y

**Question 11. ** If R is the set of real numbers and Q is the set of rational numbers, then what is
R β 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) Aβ²

(ii) Bβ²

(iii) (A βͺ C)β²

(iv) (A βͺ B)β²

(v) (Aβ²)β²

(vi) (B β C)β²

**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 β₯ 7 }

(xi) { x : x β 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 βͺ B)β² = Aβ² β© Bβ²

(ii) (A β© B)β² = Aβ² βͺ Bβ²

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

(i) (A βͺ B)β²

(ii) Aβ² β© Bβ²

(iii) (A β© B)β²,

(iv) Aβ² βͺ Bβ²

**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 60Β°, what is Aβ²?

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

(i) A βͺ Aβ² = . . .

(ii) Οβ² β© A = . . .

(iii) A β© Aβ² = . . .

(iv) Uβ² β© A = . . .

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

**Question 2. ** If X and Y are two sets such that X βͺ Y has 18 elements, X has 8 elements and
Y has 15 elements ; how many elements does X β© 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 β© T
has 11 elements, how many elements does S βͺ T have?

**Question 5. **If X and Y are two sets such that X has 40 elements, X βͺ Y has 60 elements and
X β© 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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