# 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'_{r}^{s} and to exactly 4 of Y'_{r}^{s}, 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 *2 ^{n}* subsets. Therefore, if A is a finite set having

*n*elements, then

*P(A)*has

*2*elements.

^{n}

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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