RD SHARMA Solutions for Class 11-science Maths 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:
- 4...A
- -4 ...A
- 12 ....A
- 9 ...A
- 0 .....A
- -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
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. 1.8
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
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 that
can 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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