RD SHARMA Solutions for Class 11-science Maths Chapter 1 - Sets
Chapter 1 - Sets Exercise Ex. 1.1




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
Chapter 1 - Sets Exercise Ex. 1.6
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)
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)
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)
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)
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)
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)
For any two sets A and B, prove that
B ⊂ A ∪ B
For any two sets A and B, prove that
A ∩ B ⊂ B
For any two sets A and B, prove that
A ⊂ B ⇒ A ∩ B = A
Show that For any sets A and B,
A = (A ∩ B) ∩ (A - B)
Show that For any sets A and B,
A ∪ (B - A) = A ∪ B
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.







Chapter 1 - Sets Exercise Ex. 1.7
For any two sets A and B, prove that
(A ∪ B) - B = A - B
For any two sets A and B, prove that
A- (A ∩ B) = A - B
For any two sets A and B, prove that
A - (A - B) = A ∩ B
For any two sets A and B, prove that
A ∪ (B - A) = A ∪ B
For any two sets A and B, prove that
(A - B) ∪ (A ∩ B) = A












Chapter 1 - Sets Exercise Ex. 1.2




















































Chapter 1 - Sets Exercise Ex. 1.3


















Chapter 1 - Sets Exercise Ex. 1.4






































Chapter 1 - Sets Exercise Ex. 1.5







































Chapter 1 - Sets Exercise Ex. 1.8

































Chapter 1 - Sets Exercise Ex. 1VSAQ
If a set contains n elements, then write the number of elements in its power set.
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.
Write the number of elements in the power set of null set.
If A is the void set Φ, then P(A) has just one element Φ i.e. P(Φ) ={Φ}.
Let A=and
B=.Write
.
Let A
and B be two sets having 3 and 6 elements respectively. Write the minimum
number of elements thatcan have.
The minimum number of elements thatcan have is 6.
If A= and B=
, then write A-B
and B-A.
IF A
and B are two sets such that , then write
in terms of A
and B.
Let A
and B be two sets having 4 and 7 elements respectively. Then write the
maximum number of elements that can have.
The maximum number of elements thatcan have is 11.
If A=and B=
,
then
write.
If A=and B=
, then write
.
If A and B are two sets such that n(A)=20, n(B)=25,
n()=40, then write n(
).
If A and B are two sets such that n(A)=115, n(B)=326,
n(A-B)=47, then write n().
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