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NCERT solutions Mathematics Class 11 chapter 1 Sets

Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 1 - Sets

Pages 4 - 24

Which of the following are sets? Justify our answer.

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

Q 1.1 | Page 4

Which of the following are sets? Justify our answer.

The collection of ten most talented writers of India.

Q 1.2 | Page 4

Which of the following are sets? Justify our answer.

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

Q 1.3 | Page 4

Which of the following are sets? Justify our answer.

The collection of all boys in your class.

Q 1.4 | Page 4

Which of the following are sets? Justify our answer.

The collection of all natural numbers less than 100.

Q 1.5 | Page 4

Which of the following are sets? Justify our answer.

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

Q 1.6 | Page 4

Which of the following are sets? Justify our answer.

The collection of all even integers.

Q 1.7 | Page 4

Which of the following are sets? Justify our answer.

The collection of questions in this Chapter.

Q 1.8 | Page 4

Which of the following are sets? Justify our answer.

A collection of most dangerous animals of the world.

Q 1.9 | Page 4

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?

Q 2 | Page 24

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

(1) 5…A

(2) 8…A

(3) 0…A

(4) 4…A

(5) 2…A

(6) 10…A

Q 2 | Page 5

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

Q 3.1 | Page 5

Write the following sets in roster form:

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

Q 3.2 | 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}

Q 3.3 | Page 5

Write the following sets in roster form:

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

Q 3.4 | Page 5

Write the following sets in roster form:

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

Q 3.6 | Page 5

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

Q 4.1 | Page 5

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

Q 4.2 | Page 5

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

 

Q 4.3 | Page 5

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

 

Q 4.4 | Page 5

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

Q 4.5 | Page 5

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

Q 5.1 | Page 5

List all the elements of the following sets:

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

Q 5.2 | Page 5

List all the elements of the following sets:

C = {x : x is an integer, x2 ≤ 4}

Q 5.3 | Page 5

List all the elements of the following sets:

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

Q 5.4 | Page 5

List all the elements of the following sets:

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

Q 5.5 | Page 5

List all the elements of the following sets:

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

 

Q 5.6 | 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 {xx is a prime number and a divisor of 6}
2 {2, 3} b {xx is an odd natural number less than 10}
3 {M, A,T, H, E, I,C, S} c {xx is natural number and divisor of 6}
4 {1, 3, 5, 7, 9} d {xx is a letter of the word MATHEMATICS}
Q 6 | Page 5

Write the following sets in roster form:

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

Q 305 | Page 5

Pages 8 - 9

Which of the following are examples of the null set

(i) Set of odd natural numbers divisible by 2

(ii) Set of even prime numbers

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

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

Q 1 | Page 8

Which of the following sets are finite or infinite

The set of months of a year

Q 2.1 | Page 8

Which of the following sets are finite or infinite

{1, 2, 3 ...}

Q 2.2 | Page 8

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

 

Q 2.3 | Page 8

Which of the following sets are finite or infinite

The set of positive integers greater than 100

Q 2.4 | Page 8

Which of the following sets are finite or infinite

The set of prime numbers less than 99

Q 2.5 | Page 8

State whether the following set is finite or infinite:

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

Q 3.1 | Page 8

State whether each of the following set is finite or infinite:

The set of letters in the English alphabet

Q 3.2 | Page 8

State whether each of the following set is finite or infinite:

The set of numbers which are multiple of 5

Q 3.3 | Page 8

State whether the following set is finite or infinite:

The set of animals living on the earth

Q 3.4 | Page 8

State whether each of the following set is finite or infinite:

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

Q 3.5 | Page 8

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

A = {abcd}; B = {dcba}

Q 4.1 | Page 9

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

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

Q 4.2 | Page 9

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

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

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}

Q 4.3 | Page 9

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

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

Q 4.4 | Page 9

Are the following pair of sets equal? Give reasons.

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

Q 5.1 | 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}

Q 5.2 | 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}

Q 6 | Page 9

Pages 12 - 13

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:

(i) {2, 3, 4} … {1, 2, 3, 4, 5}

(ii) {abc} … {bcd}

(iii) {xx is a student of Class XI of your school} … {xx student of your school}

(iv) {xx is a circle in the plane} … {xx is a circle in the same plane with radius 1 unit}

(v) {xx is a triangle in a plane}…{xx is a rectangle in the plane}

(vi) {xx is an equilateral triangle in a plane}… {xx is a triangle in the same plane}

(vii) {xx is an even natural number} … {xx is an integer}

Q 1 | Page 12

Examine whether the following statements are true or false: {ab} ⊄ {bca}

Q 2.1 | Page 13

Examine whether the following statements are true or false:

{ae} ⊂ {xx is a vowel in the English alphabet}

Q 2.2 | Page 13

Examine whether the following statements are true or false:

{1, 2, 3} ⊂{1, 3, 5}

Q 2.3 | Page 13

Examine whether the following statements are true or false:

{a} ⊂ {abc}

Q 2.4 | Page 13

Examine whether the following statements are true or false:

{a} ∈ (abc)

Q 2.5 | 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}

Q 2.6 | Page 13

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

Q 3 | Page 13

Write down all the subsets of the following sets:

(i) {a}

(ii) {ab}

(iii) {1, 2, 3}

(iv) Φ

Q 4 | Page 13

How many elements has P(A), if A = Φ?

Q 5 | Page 13

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

 

Q 6.1 | Page 13

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

 

Q 6.2 | Page 13

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

 

Q 6.3 | Page 13

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

 

Q 6.4 | Page 13

Write the given intervals in set-builder form:

(–3, 0)

Q 7.1 | Page 13

Write the given intervals in set-builder form:

[6, 12]

Q 7.2 | Page 13

Write the following intervals in set-builder form:

(6, 12]

Q 7.3 | Page 13

Write the following intervals in set-builder form:

[–23, 5)

Q 7.4 | Page 13

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

The set of right triangles

Q 8.1 | Page 13

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

The set of isosceles triangles

Q 8.2 | 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

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

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

Φ

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

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

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

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

Q 9.4 | Page 13

Pages 17 - 18

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

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

Q 1.1 | Page 17

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

A = {aeiou} B = {abc}

Q 1.2 | Page 17

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

A = {aeiou} B = {abc}

Q 1.2 | 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}

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}

Q 1.3 | 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}

Q 1.4 | Page 17

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

A = {1, 2, 3}, B = Φ

Q 1.5 | Page 17

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

Q 2 | Page 17

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

Q 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

(i) A ∪ B

(ii) A ∪ C

(iii) B ∪ C

(iv) B ∪ D

(v) A ∪ B ∪ C

(vi) A ∪ B ∪ D

(vii) B ∪ C ∪ D

Q 4 | Page 17

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

Q 5.1 | Page 18

Find the intersection of each pair of sets:

A = {aeiou} B = {abc}

Q 5.2 | 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}

Q 5.3 | 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}

Q 5.4 | Page 18

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

Q 5.5 | Page 18

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)

Q 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

(i) A ∩ B

(ii) A ∩ C

(iii) A ∩ D

(iv) B ∩ C

(v) B ∩ D

(vi) C ∩ D

Q 7 | 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}

Q 8.1 | Page 18

Which of the following pairs of sets are disjoint

{aeiou}and {cdef}

Q 8.2 | Page 18

Which of the following pairs of sets are disjoint

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

Q 8.3 | 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

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

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 C – D

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 D – C

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 A - C

Q 9.2 | 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

Q 9.3 | 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

Q 9.4 | 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

Q 9.5 | 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

Q 9.6 | 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

Q 9.7 | 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

 

Q 9.8 | 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

 

Q 9.9 | Page 18

If X = {abcd} and Y = {fbd, g}, find 

(i) X – Y

(ii) Y – X

(iii) X ∩ Y

Q 10 | Page 18

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

Q 11 | 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.

Q 12.1 | Page 18

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

{aeiou } and {abcd} are disjoint sets.

Q 12.2 | 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.

Q 12.3 | 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.

Q 12.4 | Page 18

Pages 20 - 21

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'

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 B'

 

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 (A ∪ C)'

 

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 ∪ B)'

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 (B -C)'

 

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')'

 

Q 1.5 | Page 20

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

A = {a, b, c}

Q 2.1 | Page 20

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

B = {d, e, f, g}

 

Q 2.2 | Page 20

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

C = {a, c, e, g}

Q 2.3 | Page 20

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

D = {fgha}

Q 2.4 | Page 20

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

(i) {xx is an even natural number}

(ii) {xx is an odd natural number}

(iii) {xx is a positive multiple of 3}

(iv) {xx is a prime number}

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

(vi) {xx is a perfect square}

(vii) {xx is perfect cube}

(viii) {xx + 5 = 8}

(ix) {x: 2x + 5 = 9}

(x) {xx ≥ 7}

(xi) {xx ∈ N and 2x + 1 > 10}

Q 3 | 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'

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'

Q 4.2 | Page 20

Draw appropriate Venn diagram for  the following:

(A ∪ B)'

Q 5.1 | Page 20

Draw appropriate Venn diagram for the following:

A' ∩ B'

Q 5.2 | Page 20

Draw appropriate Venn diagram for the following:

(A ∩ B)'

Q 5.3 | Page 20

Draw appropriate Venn diagram for the following:

A' ∪ B'

Q 5.4 | 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'

Q 6 | Page 20

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

A ∪ A' = ....

Q 7.1 | Page 21

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

Φ′ ∩ A = …

Q 7.2 | Page 21

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

A ∩ A' =....

Q 7.3 | Page 21

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

U' ∩ A = ...

Q 7.4 | Page 21

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).

Q 1 | 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?

Q 3 | 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?

Q 4 | 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?

Q 5 | 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?

Q 6 | 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?

Q 7 | 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?

Q 8 | Page 24

Pages 26 - 27

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}.

Q 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

Q 2.1 | 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

Q 2.2 | 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

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

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 x ∈ A and A ⊄ B, then x ∈ B

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 A ⊂ B and x ∉ B, then x ∉ A

Q 2.6 | 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.

Q 3 | 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

Q 4 | Page 26

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

Q 5 | Page 26

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

Q 6 | Page 26

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

Q 7 | Page 26

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

Q 8 | Page 27

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

Q 9.1 | Page 27

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

 

Q 9.2 | Page 27

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

Q 10 | 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)

Q 11 | 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.

Q 12 | 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?

Q 13 | 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?

Q 14 | 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.

Q 15 | 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.

Q 16 | Page 27

NCERT Mathematics Class 11

Mathematics Textbook for Class 11
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