# RD Sharma Solution Class 11 Mathematics Chapter 1 Sets

## Chapter 1 – Sets Exercise Ex. 1.1

Question 1
Solution 1
Question 2
Solution 2
Question 3

If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then insert the appropriate symbol or in each of the following blank spaces:

1. 4…A
2. -4 …A
3. 12 ….A
4. 9 …A
5. 0 …..A
6. -12 ….A
Solution 3

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22

Solution 22

Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9

Question 1

Solution 1

Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16

Solution 16

Question 17
Solution 17
Question 18
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17
Question 18
Solution 18
Question 19

Solution 19

Question 20
Solution 20

## Chapter 1 – Sets Exercise Ex. 1.6

Question 1

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify the following identities:

A (B C) = (A B) (A C)

Solution 1

Question 2

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify the following identities:

A (B C) = (A B) (A C)

Solution 2

Question 3

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify the following identities:

A (B – C) = (A B) – (A C)

Solution 3

Question 4

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify the following identities:

A – (B C) = (A – B) (A – C)

Solution 4

Question 5

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify the following identities:

A – (B C) = (A – B) (A – C)

Solution 5

Question 6

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}.
Verify the following identities:

A (B D C) = (A B) D (A C)

Solution 6

Question 7

For any two sets A and B, prove that

B A B

Solution 7

Question 8

For any two sets A and B, prove that

A B B

Solution 8

Question 9

For any two sets A and B, prove that

A B A B = A

Solution 9

Question 10

Show that For any sets A and B,

A = (A B) (A – B)

Solution 10

Question 11

Show that For any sets A and B,

A (B – A) = A B

Solution 11

Question 12

Each set X, contains 5 elements and each set Y,
contains 2 elements and each element of S belongs to exactly 10 of the X’rs and to exactly 4 of Y’rs, then find the value of n.

Solution 12

Question 13
Solution 13
Question 14
Solution 14
Question 15
Solution 15
Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Solution 24

Question 25

Solution 25

Question 26

Solution 26

## Chapter 1 – Sets Exercise Ex. 1.7

Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7

For any two sets A and B, prove that

(A B) – B = A – B

Solution 7

Question 8

For any two sets A and B, prove that

A- (A B) = A – B

Solution 8

Question 9

For any two sets A and B, prove that

A – (A – B) = A B

Solution 9

Question 10

For any two sets A and B, prove that

A (B – A) = A B

Solution 10

Question 11

For any two sets A and B, prove that

(A – B) (A B) = A

Solution 11

Question 1

Solution 1

Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7

Solution 7

Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11

Question 12
Solution 12
Question 13
Solution 13
Question 14
Solution 14

Question 15
Solution 15
Question 16
Solution 16
Question 17
Solution 17

## Chapter 1 – Sets Exercise Ex. 1VSAQ

Question 1

If a set contains n elements, then write the number of
elements in its power set.

Solution 1

Let A be a
set. Then collection or family of all subsets of A is called the power set of A
and is denoted by P(A).

A set having n elements has 2n subsets. Therefore, if A is a finite set having n elements, then P(A) has 2n elements.

Question 2

Write the number of
elements in the power set of null set.

Solution 2

If A is
the void set Φ, then P(A) has just one element Φ i.e. P(Φ) ={Φ}.

Question 3

Let A=and

B=.Write.

Solution 3

Question 4

Let A
and B be two sets having 3 and 6 elements respectively. Write the minimum
number of elements thatcan have.

Solution 4

The minimum number of elements thatcan have is 6.

Question 5

If A= and B=, then write A-B
and B-A.

Solution 5

Question 6

IF A
and B are two sets such that , then write  in terms of A
and B.

Solution 6

Question 7

Let A
and B be two sets having 4 and 7 elements respectively. Then write the
maximum number of elements that can have.

Solution 7

The maximum number of elements thatcan have is 11.

Question 8

If A=and B=,

then
write.

Solution 8

Question 9

If A=and B=, then write.

Solution 9

Question 10

If A and B are two sets such that n(A)=20,
n(B)=25,

n()=40, then write n().

Solution 10

Question 11

If A and B are two sets such that n(A)=115, n(B)=326,
n(A-B)=47, then write n().

Solution 11

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