# RD SHARMA Solutions for Class 11-science Maths Chapter 1 - Sets

Page / Exercise

## 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

## Chapter 1 - Sets Exercise Ex. 1.6

Question 2(i)

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(i)

Question 2(ii)

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(ii)

Question 2(iii)

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(iii)

Question 2(iv)

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(iv)

Question 2(v)

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(v)

Question 2(vi)

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 2(vi)

Question 4(i)

For any two sets A and B, prove that

B A B

Solution 4(i)

Question 4(ii)

For any two sets A and B, prove that

A B B

Solution 4(ii)

Question 4(iii)

For any two sets A and B, prove that

A B A B = A

Solution 4(iii)

Question 14(i)

Show that For any sets A and B,

A = (A B) (A - B)

Solution 14(i)

Question 14(ii)

Show that For any sets A and B,

A (B - A) = A B

Solution 14(ii)

Question 15

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 15

Question 1
Solution 1
Question 3(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Question 5

Solution 5

Question 6(i)

Solution 6(i)

Question 6(ii)

Solution 6(ii)

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12(i)

Solution 12(i)

Question 12(ii)

Solution 12(ii)

Question 13

Solution 13

## Chapter 1 - Sets Exercise Ex. 1.7

Question 4(i)

For any two sets A and B, prove that

(A B) - B = A - B

Solution 4(i)

Question 4(ii)

For any two sets A and B, prove that

A- (A B) = A - B

Solution 4(ii)

Question 4(iii)

For any two sets A and B, prove that

A - (A - B) = A B

Solution 4(iii)

Question 4(iv)

For any two sets A and B, prove that

A (B - A) = A B

Solution 4(iv)

Question 4(v)

For any two sets A and B, prove that

(A - B) (A B) = A

Solution 4(v)

Question 1
Solution 1
Question 2(i)
Solution 2(i)
Question 2(ii)
Solution 2(ii)
Question 2(iii)
Solution 2(iii)
Question 2(iv)
Solution 2(iv)
Question 3
Solution 3

Question 1(i)
Solution 1(i)
Question 1(ii)
Solution 1(ii)
Question 1(iii)
Solution 1(iii)
Question 1(iv)

Solution 1(iv)
Question 1(v)
Solution 1(v)
Question 1(vi)
Solution 1(vi)
Question 1(vii)
Solution 1(vii)
Question 1(viii)
Solution 1(viii)
Question 1(ix)
Solution 1(ix)
Question 2(i)
Solution 2(i)
Question 2(ii)
Solution 2(ii)
Question 2(iii)
Solution 2(iii)
Question 2(iv)
Solution 2(iv)
Question 2(v)
Solution 2(v)
Question 2(vi)
Solution 2(vi)
Question 2(vii)
Solution 2(vii)
Question 2(viii)
Solution 2(viii)
Question 3(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Question 3(iii)
Solution 3(iii)
Question 3(iv)
Solution 3(iv)
Question 3(v)

Solution 3(v)

Question 3(vi)
Solution 3(vi)
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 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
Solution 7
Question 8
Solution 8
Question 9
Solution 9

Question 1

Solution 1

Question 2
Solution 2
Question 3
Solution 3
Question 4(i)

Solution 4(i)

Question 4(ii)
Solution 4(ii)
Question 4(iii)
Solution 4(iii)
Question 4(iv)
Solution 4(iv)
Question 4(v)
Solution 4(v)
Question 4(vi)
Solution 4(vi)
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 1
Solution 1
Question 2(i)
Solution 2(i)
Question 2(ii)
Solution 2(ii)
Question 2(iii)
Solution 2(iii)
Question 2(iv)
Solution 2(iv)
Question 2(v)
Solution 2(v)
Question 2(vi)
Solution 2(vi)
Question 2(vii)
Solution 2(vii)
Question 2(viii)
Solution 2(viii)
Question 2(ix)
Solution 2(ix)
Question 2(x)
Solution 2(x)
Question 3(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Question 3(iii)
Solution 3(iii)
Question 3(iv)
Solution 3(iv)
Question 3(v)
Solution 3(v)
Question 3(vi)
Solution 3(vi)
Question 4
Solution 4
Question 5

Solution 5

Question 6
Solution 6

Question 1

Solution 1

Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5(i)
Solution 5(i)
Question 5(ii)
Solution 5(ii)
Question 5(iii)

Solution 5(iii)

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

## 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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