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# NCERT solutions for Class 11 Mathematics chapter 1 - Sets

## Chapter 1: Sets

Ex. 1.10Ex. 1.20Ex. 1.30Ex. 1.40Ex. 1.50Ex. 1.60Ex. 1.70

#### Chapter 1: Sets Exercise 1.10 solutions [Pages 4 - 5]

Ex. 1.10 | Q 1.1 | Page 4

Which of the following are sets? Justify our answer.

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

Ex. 1.10 | Q 1.2 | Page 4

Which of the following are sets? Justify our answer.

The collection of ten most talented writers of India.

Ex. 1.10 | Q 1.3 | Page 4

Which of the following are sets? Justify our answer.

A team of eleven best-cricket batsmen of the world.

Ex. 1.10 | Q 1.4 | Page 4

Which of the following are sets? Justify our answer.

The collection of all boys in your class.

Ex. 1.10 | Q 1.5 | Page 4

Which of the following are sets? Justify our answer.

The collection of all natural numbers less than 100.

Ex. 1.10 | Q 1.6 | Page 4

Which of the following are sets? Justify our answer.

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

Ex. 1.10 | Q 1.7 | Page 4

Which of the following are sets? Justify our answer.

The collection of all even integers.

Ex. 1.10 | Q 1.8 | Page 4

Which of the following are sets? Justify our answer.

The collection of questions in this Chapter.

Ex. 1.10 | Q 1.9 | Page 4

Which of the following are sets? Justify our answer.

A collection of most dangerous animals of the world.

Ex. 1.10 | Q 2.1 | Page 5

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

5…A

Ex. 1.10 | Q 2.2 | Page 5

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

8…A

Ex. 1.10 | Q 2.3 | Page 5

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

0…A

Ex. 1.10 | Q 2.4 | Page 5

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

4…A

Ex. 1.10 | Q 2.5 | Page 5

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

2…A

Ex. 1.10 | Q 2.6 | Page 5

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

10…A

Ex. 1.10 | Q 3.1 | Page 5

Write the following sets in roster form: A = {xx is an integer and –3 < < 7}.

Ex. 1.10 | Q 3.2 | Page 5

Write the following sets in roster form:

B = {xx is a natural number less than 6}.

Ex. 1.10 | Q 3.3 | Page 5

Write the following sets in roster form:

C = {xx is a two-digit natural number such that the sum of its digits is 8}

Ex. 1.10 | Q 3.4 | Page 5

Write the following sets in roster form:

D = {xx is a prime number which is divisor of 60}.

Ex. 1.10 | Q 3.4 | Page 5

Write the following sets in roster form:

D = {xx is a prime number which is divisor of 60}.

Ex. 1.10 | Q 3.5 | Page 5

Write the following sets in roster form:

E = The set of all letters in the word TRIGONOMETRY.

Ex. 1.10 | Q 3.6 | Page 5

Write the following sets in roster form:

F = The set of all letters in the word BETTER.

Ex. 1.10 | Q 4.1 | Page 5

Write the following sets in the set-builder form: (3, 6, 9, 12)

Ex. 1.10 | Q 4.2 | Page 5

Write the following sets in the set-builder form: {2, 4, 8, 16, 32}

Ex. 1.10 | Q 4.3 | Page 5

Write the following sets in the set-builder form: {5, 25, 125, 625}

Ex. 1.10 | Q 4.4 | Page 5

Write the following sets in the set-builder form: {2, 4, 6 …}

Ex. 1.10 | Q 4.5 | Page 5

Write the following sets in the set-builder form:  {1, 4, 9 … 100}

Ex. 1.10 | Q 5.1 | Page 5

List all the elements of the sets: A = {xx is an odd natural number}

Ex. 1.10 | Q 5.2 | Page 5

List all the elements of the following sets:

B = {xx is an integer, -1/2 < x < 9/2}

Ex. 1.10 | Q 5.3 | Page 5

List all the elements of the following sets:

C = {x : x is an integer, x2 ≤ 4}

Ex. 1.10 | Q 5.4 | Page 5

List all the elements of the following sets:

D = {xx is a letter in the word “LOYAL”}

Ex. 1.10 | Q 5.5 | Page 5

List all the elements of the following sets:

E = {xx is a month of a year not having 31 days}

Ex. 1.10 | Q 5.6 | Page 5

List all the elements of the following sets:

F = {xx is a consonant in the English alphabet which proceeds k}.

Ex. 1.10 | Q 6 | Page 5

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

 1 {1, 2, 3, 6} a {x: x is a prime number and a divisor of 6} 2 {2, 3} b {x: x is an odd natural number less than 10} 3 {M, A,T, H, E, I,C, S} c {x: x is natural number and divisor of 6} 4 {1, 3, 5, 7, 9} d {x: x is a letter of the word MATHEMATICS}

#### Chapter 1: Sets Exercise 1.20 solutions [Pages 8 - 9]

Ex. 1.20 | Q 1.1 | Page 8

Which of the following are examples of the null set

Set of odd natural numbers divisible by 2

Ex. 1.20 | Q 1.2 | Page 8

Which of the following are examples of the null set

Set of even prime numbers

Ex. 1.20 | Q 1.3 | Page 8

Which of the following are examples of the null set

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

Ex. 1.20 | Q 1.4 | Page 8

Which of the following are examples of the null set

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

Ex. 1.20 | Q 2.1 | Page 8

Which of the following sets are finite or infinite

The set of months of a year

Ex. 1.20 | Q 2.2 | Page 8

Which of the following sets are finite or infinite

{1, 2, 3 ...}

Ex. 1.20 | Q 2.3 | Page 8

Which of the following sets are finite or infinite  {1, 2, 3 ... 99, 100}

Ex. 1.20 | Q 2.4 | Page 8

Which of the following sets are finite or infinite

The set of positive integers greater than 100

Ex. 1.20 | Q 2.5 | Page 8

Which of the following sets are finite or infinite

The set of prime numbers less than 99

Ex. 1.20 | Q 3.1 | Page 8

State whether the following set is finite or infinite:

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

Ex. 1.20 | Q 3.2 | Page 8

State whether the following set is finite or infinite:

The set of letters in the English alphabet

Ex. 1.20 | Q 3.3 | Page 8

State whether the following set is finite or infinite:

The set of numbers which are multiple of 5

Ex. 1.20 | Q 3.4 | Page 8

State whether the following set is finite or infinite:

The set of animals living on the earth

Ex. 1.20 | Q 3.5 | Page 8

State whether the following set is finite or infinite:

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

Ex. 1.20 | Q 4.1 | Page 9

In the following, state whether A = B or not:

A = {abcd}; B = {dcba}

Ex. 1.20 | Q 4.2 | Page 9

In the following, state whether A = B or not:

A = {4, 8, 12, 16}; B = {8, 4, 16, 18}

Ex. 1.20 | Q 4.3 | Page 9

In the following, state whether A = B or not:

A = {2, 4, 6, 8, 10}; B = {xis positive even integer and ≤ 10}

Ex. 1.20 | Q 4.4 | Page 9

In the following, state whether A = B or not:

A = {xis a multiple of 10}; B = {10, 15, 20, 25, 30 ...}

Ex. 1.20 | Q 5.1 | Page 9

Are the following pair of sets equal? Give reasons.

A = {2, 3}; B = {xis solution of x2 + 5+ 6 = 0}

Ex. 1.20 | Q 5.2 | Page 9

Are the following pair of sets equal? Give reasons.

A = {xis a letter in the word FOLLOW}; B = {yis a letter in the word WOLF}

Ex. 1.20 | Q 6 | Page 9

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}

#### Chapter 1: Sets Exercise 1.30 solutions [Pages 12 - 13]

Ex. 1.30 | Q 1.1 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{2, 3, 4} … {1, 2, 3, 4, 5}

Ex. 1.30 | Q 1.2 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{a, b, c} … {b, c, d}

Ex. 1.30 | Q 1.3 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x: x is a student of Class XI of your school} … {x: x student of your school}

Ex. 1.30 | Q 1.4 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}

Ex. 1.30 | Q 1.5 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x: x is a triangle in a plane}…{x: x is a rectangle in the plane}

Ex. 1.30 | Q 1.6 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x: x is an equilateral triangle in a plane}… {x: x is a triangle in the same plane}

Ex. 1.30 | Q 1.7 | Page 12

Make correct statement by filling in the symbols ⊂ or ⊄ in the blank space:

{x: x is an even natural number} … {x: x is an integer}

Ex. 1.30 | Q 2.1 | Page 13

Examine whether the following statement is true or false: {a, b} ⊄ {b, c, a}

• True

• False

Ex. 1.30 | Q 2.2 | Page 13

Examine whether the following statement is true or false:

{a, e} ⊂ {x: x is a vowel in the English alphabet}

• True

• False

Ex. 1.30 | Q 2.3 | Page 13

Examine whether the following statement is true or false:

{1, 2, 3} ⊂{1, 3, 5}

• True

• False

Ex. 1.30 | Q 2.4 | Page 13

Examine whether the following statement is true or false:

{a} ⊂ {a. b, c}

• True

• False

Ex. 1.30 | Q 2.5 | Page 13

Examine whether the following statement is true or false:

{a} ∈ (a, b, c)

• True

• False

Ex. 1.30 | Q 2.6 | Page 13

Examine whether the following statements are true or false:

{xx is an even natural number less than 6} ⊂ {xx is a natural number which divides 36}

• True

• False

Ex. 1.30 | Q 3.01 | Page 13

Let A= {1, 2, {3, 4,}, 5}. Which of the following statement is incorrect and why?

{3, 4}⊂ A

Ex. 1.30 | Q 3.02 | Page 13

Let A= {1, 2, {3, 4,}, 5}. Which of the following statement is incorrect and why?

{3, 4}}∈ A

Ex. 1.30 | Q 3.03 | Page 13

Let A= {1, 2, {3, 4,}, 5}. Which of the following statement Is incorrect and why?

{{3, 4}}⊂ A

Ex. 1.30 | Q 3.04 | Page 12

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

1∈ A

Ex. 1.30 | Q 3.05 | Page 12

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

1⊂ A

Ex. 1.30 | Q 3.06 | Page 13

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

{1, 2, 5} ⊂ A

Ex. 1.30 | Q 3.07 | Page 13

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

{1, 2, 5} ∈ A

Ex. 1.30 | Q 3.08 | Page 13

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

{1, 2, 3} ⊂ A

Ex. 1.30 | Q 3.09 | Page 13

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

Φ ∈ A

Ex. 1.30 | Q 3.1 | Page 13

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

Φ ⊂ A

Ex. 1.30 | Q 3.11 | Page 13

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

{Φ} ⊂ A

Ex. 1.30 | Q 4.1 | Page 13

Write down all the subsets of the following set:

{a}

Ex. 1.30 | Q 4.2 | Page 13

Write down all the subsets of the following sets:

{a, b}

Ex. 1.30 | Q 4.3 | Page 13

Write down all the subsets of the following sets:

{1, 2, 3}

Ex. 1.30 | Q 4.4 | Page 13

Write down all the subsets of the following sets:

Φ

Ex. 1.30 | Q 5 | Page 13

How many elements has P(A), if A = Φ?

Ex. 1.30 | Q 6.1 | Page 13

Write the following as intervals: {xx ∈ R, –4 < x ≤ 6}

Ex. 1.30 | Q 6.2 | Page 13

Write the following as intervals:  {xx ∈ R, –12 < x < –10}

Ex. 1.30 | Q 6.3 | Page 13

Write the following as intervals: {xx ∈ R, 0 ≤ x < 7}

Ex. 1.30 | Q 6.4 | Page 13

Write the following as intervals:  {xx ∈ R, 3 ≤ x ≤ 4}

Ex. 1.30 | Q 7.1 | Page 13

Write the given intervals in set-builder form:

(–3, 0)

Ex. 1.30 | Q 7.2 | Page 13

Write the given intervals in set-builder form:

[6, 12]

Ex. 1.30 | Q 7.3 | Page 13

Write the following intervals in set-builder form:

(6, 12]

Ex. 1.30 | Q 7.4 | Page 13

Write the following intervals in set-builder form:

[–23, 5)

Ex. 1.30 | Q 8.1 | Page 13

What universal set (s) would you propose for the following:

The set of right triangles

Ex. 1.30 | Q 8.2 | Page 13

What universal set (s) would you propose for the following:

The set of isosceles triangles

Ex. 1.30 | Q 9.1 | Page 13

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 universals set (s) for all the three sets A, B and C

{0, 1, 2, 3, 4, 5, 6}

Ex. 1.30 | Q 9.2 | Page 13

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 universals set (s) for all the three sets A, B and C

Φ

Ex. 1.30 | Q 9.3 | Page 13

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 universals set (s) for all the three sets A, B and C

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

Ex. 1.30 | Q 9.4 | Page 13

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 universals set (s) for all the three sets A, B and C

{1, 2, 3, 4, 5, 6, 7, 8}

#### Chapter 1: Sets Exercise 1.40 solutions [Pages 17 - 18]

Ex. 1.40 | Q 1.1 | Page 17

Find the union of each of the following pairs of sets:

X = {1, 3, 5} Y = {1, 2, 3}

Ex. 1.40 | Q 1.2 | Page 17

Find the union of each of the following pairs of sets:

A = {aeiou} B = {abc}

Ex. 1.40 | Q 1.3 | Page 17

Find the union of each of the following pairs of sets:

A = {xx is a natural number and multiple of 3} B = {xx is a natural number less than 6}

Ex. 1.40 | Q 1.4 | Page 17

Find the union of each of the following pairs of sets:

A = {xx is a natural number and 1 < x ≤ 6}  B = {xx is a natural number and 6 < x < 10}

Ex. 1.40 | Q 1.5 | Page 17

Find the union of each of the following pairs of sets:

A = {1, 2, 3}, B = Φ

Ex. 1.40 | Q 2 | Page 17

Let A = {ab}, B = {abc}. Is A ⊂ B? What is A ∪ B?

Ex. 1.40 | Q 3 | Page 17

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

Ex. 1.40 | Q 4.1 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B

Ex. 1.40 | Q 4.2 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ C

Ex. 1.40 | Q 4.3 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ C

Ex. 1.40 | Q 4.4 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ D

Ex. 1.40 | Q 4.5 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B ∪ C

Ex. 1.40 | Q 4.6 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B ∪ D

Ex. 1.40 | Q 4.7 | Page 17

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

B ∪ C ∪ D

Ex. 1.40 | Q 5.1 | Page 18

Find the intersection of each pair of sets: X = {1, 3, 5} Y = {1, 2, 3}

Ex. 1.40 | Q 5.2 | Page 18

Find the intersection of each pair of sets:

A = {aeiou} B = {abc}

Ex. 1.40 | Q 5.3 | Page 18

Find the intersection of each pair of sets:

A = {xx is a natural number and multiple of 3} B = {xx is a natural number less than 6}

Ex. 1.40 | Q 5.4 | Page 18

Find the intersection of each pair of sets:

A = {xx is a natural number and 1 < x ≤ 6} B = {xx is a natural number and 6 < x < 10}

Ex. 1.40 | Q 5.5 | Page 18

Find the intersection of each pair of sets:  A = {1, 2, 3}, B = Φ

Ex. 1.40 | Q 6.01 | Page 18

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

A ∩ B

Ex. 1.40 | Q 6.02 | Page 18

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

B ∩ C

Ex. 1.40 | Q 6.03 | Page 18

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

A ∩ C ∩ D

Ex. 1.40 | Q 6.04 | Page 18

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

A ∩ C

Ex. 1.40 | Q 6.05 | Page 18

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

B ∩ D

Ex. 1.40 | Q 6.06 | Page 18

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

A ∩ (B ∪ C)

Ex. 1.40 | Q 6.07 | Page 18

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

A ∩ D

Ex. 1.40 | Q 6.08 | Page 18

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

A ∩ (B ∪ D)

Ex. 1.40 | Q 6.09 | Page 18

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

(A ∩ B) ∩ (B ∪ C)

Ex. 1.40 | Q 6.1 | Page 18

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

(A ∪ D) ∩ (B ∪ C)

Ex. 1.40 | Q 7.1 | Page 18

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

A ∩ B

Ex. 1.40 | Q 7.2 | Page 18

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

A ∩ C

Ex. 1.40 | Q 7.3 | Page 18

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

A ∩ D

Ex. 1.40 | Q 7.4 | Page 18

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

B ∩ C

Ex. 1.40 | Q 7.5 | Page 18

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

B ∩ D

Ex. 1.40 | Q 7.6 | Page 18

If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

C ∩ D

Ex. 1.40 | Q 8.1 | Page 18

Which of the following pairs of sets are disjoint

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

Ex. 1.40 | Q 8.2 | Page 18

Which of the following pairs of sets are disjoint

{aeiou}and {cdef}

Ex. 1.40 | Q 8.3 | Page 18

Which of the following pairs of sets are disjoint

{x: x is an even integer} and {x: x is an odd integer}

Ex. 1.40 | Q 9.01 | Page 18

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 A – B

Ex. 1.40 | Q 9.02 | Page 18

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 A - C

Ex. 1.40 | Q 9.03 | Page 18

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 A – D

Ex. 1.40 | Q 9.04 | Page 18

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 B – A

Ex. 1.40 | Q 9.05 | Page 18

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 C – A

Ex. 1.40 | Q 9.06 | Page 18

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 D – A

Ex. 1.40 | Q 9.07 | Page 18

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 B – C

Ex. 1.40 | Q 9.08 | Page 18

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 B – D

Ex. 1.40 | Q 9.09 | Page 18

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 C – B

Ex. 1.40 | Q 9.1 | Page 18

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 D – B

Ex. 1.40 | Q 9.11 | Page 18

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 C – D

Ex. 1.40 | Q 9.12 | Page 18

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 D – C

Ex. 1.40 | Q 10.1 | Page 18

If X = {a, b, c, d} and Y = {f, b, d, g}, find

X – Y

Ex. 1.40 | Q 10.2 | Page 18

If X = {a, b, c, d} and Y = {f, b, d, g}, find

Y – X

Ex. 1.40 | Q 10.3 | Page 18

If X = {a, b, c, d} and Y = {f, b, d, g}, find

X ∩ Y

Ex. 1.40 | Q 11 | Page 18

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

Ex. 1.40 | Q 12.1 | Page 18

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

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

Ex. 1.40 | Q 12.2 | Page 18

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

{aeiou } and {abcd} are disjoint sets.

Ex. 1.40 | Q 12.3 | Page 18

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

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

Ex. 1.40 | Q 12.4 | Page 18

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

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

#### Chapter 1: Sets Exercise 1.50 solutions [Pages 20 - 21]

Ex. 1.50 | Q 1.1 | Page 20

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 A'

Ex. 1.50 | Q 1.2 | Page 20

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 B'

Ex. 1.50 | Q 1.3 | Page 20

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 (A ∪ C)'

Ex. 1.50 | Q 1.4 | Page 20

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 (A ∪ B)'

Ex. 1.50 | Q 1.5 | Page 20

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 (A')'

Ex. 1.50 | Q 1.6 | Page 20

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 (B -C)'

Ex. 1.50 | Q 2.1 | Page 20

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

A = {a, b, c}

Ex. 1.50 | Q 2.2 | Page 20

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

B = {d, e, f, g}

Ex. 1.50 | Q 2.3 | Page 20

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

C = {a, c, e, g}

Ex. 1.50 | Q 2.4 | Page 20

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

D = {fgha}

Ex. 1.50 | Q 3.01 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is an even natural number}

Ex. 1.50 | Q 3.02 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is an odd natural number}

Ex. 1.50 | Q 3.03 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is a positive multiple of 3}

Ex. 1.50 | Q 3.04 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is a prime number}

Ex. 1.50 | Q 3.05 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is a natural number divisible by 3 and 5}

Ex. 1.50 | Q 3.06 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is a perfect square}

Ex. 1.50 | Q 3.07 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx is perfect cube}

Ex. 1.50 | Q 3.08 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx + 5 = 8}

Ex. 1.50 | Q 3.09 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{x: 2x + 5 = 9}

Ex. 1.50 | Q 3.1 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx ≥ 7}

Ex. 1.50 | Q 3.11 | Page 20

Taking the set of natural numbers as the universal set, write down the complements of the following sets:

{xx ∈ N and 2x + 1 > 10}

Ex. 1.50 | Q 4.1 | Page 20

If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (A ∪ B)' = A' ∩ B'

Ex. 1.50 | Q 4.2 | Page 20

If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that (A ∩ B)' = A' ∪ B'

Ex. 1.50 | Q 5.1 | Page 20

Draw appropriate Venn diagram for  the following:

(A ∪ B)'

Ex. 1.50 | Q 5.2 | Page 20

Draw appropriate Venn diagram for the following:

A' ∩ B'

Ex. 1.50 | Q 5.3 | Page 20

Draw appropriate Venn diagram for the following:

(A ∩ B)'

Ex. 1.50 | Q 5.4 | Page 20

Draw appropriate Venn diagram for the following:

A' ∪ B'

Ex. 1.50 | Q 6 | Page 20

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'

Ex. 1.50 | Q 7.1 | Page 21

Fill in the blanks to make each of the following a true statement:

A ∪ A' = ....

Ex. 1.50 | Q 7.2 | Page 21

Fill in the blanks to make each of the following a true statement:

Φ′ ∩ A = …

Ex. 1.50 | Q 7.3 | Page 21

Fill in the blanks to make each of the following a true statement:

A ∩ A' =....

Ex. 1.50 | Q 7.4 | Page 21

Fill in the blanks to make each of the following a true statement:

U' ∩ A = ...

#### Chapter 1: Sets Exercise 1.60 solutions [Page 24]

Ex. 1.60 | Q 1 | Page 24

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

Ex. 1.60 | Q 2 | Page 24

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?

Ex. 1.60 | Q 3 | Page 24

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

Ex. 1.60 | Q 4 | Page 24

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?

Ex. 1.60 | Q 5 | Page 24

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?

Ex. 1.60 | Q 6 | Page 24

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?

Ex. 1.60 | Q 7 | Page 24

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?

Ex. 1.60 | Q 8 | Page 24

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?

#### Chapter 1: Sets Exercise 1.70 solutions [Pages 26 - 27]

Ex. 1.70 | Q 1 | Page 26

Decide, among the following sets, which sets are subsets of one and another:

A = {xx ∈ R and x satisfy x2 – 8x + 12 = 0}, B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.

Ex. 1.70 | Q 2.1 | Page 26

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If x ∈ A and A ∈ B, then x ∈ B

Ex. 1.70 | Q 2.2 | Page 26

In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and B ∈ C, then A ∈ C

Ex. 1.70 | Q 2.3 | Page 26

determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and B ⊂ C, then A ⊂ C

Ex. 1.70 | Q 2.4 | Page 26

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊄ B and B ⊄ C, then A ⊄ C

Ex. 1.70 | Q 2.5 | Page 26

determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If x ∈ A and A ⊄ B, then x ∈ B

Ex. 1.70 | Q 2.6 | Page 26

Determine whether the statement is true or false. If it is true, prove it. If it is false, give an example.

If A ⊂ B and x ∉ B, then x ∉ A

Ex. 1.70 | Q 3 | Page 26

Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. show that B = C.

Ex. 1.70 | Q 4 | Page 26

Show that the following four conditions are equivalent:

(i) A ⊂ B

(ii) A – B = Φ

(iii) A ∪ B = B

(iv) A ∩ B = A

Ex. 1.70 | Q 5 | Page 26

Show that if A ⊂ B, then C – B ⊂ C – A.

Ex. 1.70 | Q 6 | Page 26

Assume that P (A) = P (B). Show that A = B.

Ex. 1.70 | Q 7 | Page 26

Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer.

Ex. 1.70 | Q 8 | Page 27

Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

Ex. 1.70 | Q 9.1 | Page 27

Using properties of sets show that A ∪ (A ∩ B) = A

Ex. 1.70 | Q 9.2 | Page 27

Using properties of sets show that A ∩ (A ∪ B) = A.

Ex. 1.70 | Q 10 | Page 27

Show that A ∩ B = A ∩ C need not imply B = C.

Ex. 1.70 | Q 11 | Page 27

Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X, show that A = B.

(Hints A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law)

Ex. 1.70 | Q 12 | Page 27

Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = Φ.

Ex. 1.70 | Q 13 | Page 27

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Ex. 1.70 | Q 14 | Page 27

In a group of students 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Ex. 1.70 | Q 15 | Page 27

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I,11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find:

(i) the number of people who read at least one of the newspapers.

(ii) the number of people who read exactly one newspaper.

Ex. 1.70 | Q 16 | Page 27

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

## Chapter 1: Sets

Ex. 1.10Ex. 1.20Ex. 1.30Ex. 1.40Ex. 1.50Ex. 1.60Ex. 1.70

## NCERT solutions for Class 11 Mathematics chapter 1 - Sets

NCERT solutions for Class 11 Maths chapter 1 (Sets) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Textbook for Class 11 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics chapter 1 Sets are Practical Problems on Union and Intersection of Two Sets, Power Set, Subsets, Equal Sets, Finite and Infinite Sets, The Empty Set, Sets and Their Representations, Complement of a Set, Union Set, Venn Diagrams, Universal Set, Proper and Improper Subset, Open and Close Intervals, Operation on Set - Disjoint Sets, Intersection of Sets, Difference of Sets, Element Count Set, Intrdouction of Operations on Sets.

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