RD SHARMA SOLUTION CHAPTER- 1 Sets I CLASS 11TH MATHEMATICS-EDUGROWN

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. 1.2

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

Chapter 1 Sets Exercise Ex. 1.3

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

Chapter 1 Sets Exercise Ex. 1.4

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

Chapter 1 Sets Exercise Ex. 1.5

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

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 ∪ BSolution 4(i)

Question 4(ii)

For any two sets A and B, prove that

A ∩ B ⊂ BSolution 4(ii)

Question 4(iii)

For any two sets A and B, prove that

A ⊂ B ⇒ A ∩ B = ASolution 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 ∪ BSolution 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’_r^s and to exactly 4 of Y’_r^s, 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 – BSolution 4(i)

Question 4(ii)

For any two sets A and B, prove that

A- (A ∩ B) = A – BSolution 4(ii)

Question 4(iii)

For any two sets A and B, prove that

A – (A – B) = A ∩ BSolution 4(iii)

Question 4(iv)

For any two sets A and B, prove that

A ∪ (B – A) = A ∪ BSolution 4(iv)

Question 4(v)

For any two sets A and B, prove that

(A – B) ∪ (A ∩ B) = ASolution 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

Chapter 1 Sets Exercise Ex. 1.8

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