CBSE NCERT Solutions For Class 11th Maths Chapter 1 : Set. NCERT Solutins For Class 11 Mathematics. Exercise 1.1, Exercise 1.2, Exercise 1.3, Exercise 1.4, Exercise 1.5, Exercise 1.6, (Miscellaneous Excercise) many more solutions

**Exercise 1.4**

**Question 1:**

Find the union of each of the following pairs of sets:

- X = {1, 3, 5} Y = {1, 2, 3}
- A = {
*a*,*e*,*i*,*o*,*u*} B = {*a*,*b*,*c*} - A = {
*x*:*x*is a natural number and multiple of 3} B = {*x*:*x*is a natural number less than 6} - A = {
*x*:*x*is a natural number and 1 <*x*≤ 6}

B = {*x*: *x* is a natural number and 6 < *x* < 10}

**(v) **A = {1, 2, 3}, B = Φ

Answer

- X = {1, 3, 5} Y = {1, 2, 3} X∪ Y= {1, 2, 3, 5}
- A = {
*a*,*e*,*i*,*o*,*u*} B = {*a*,*b*,*c*}

A∪ B = {*a*, *b*, *c*, *e*, *i*, *o*, *u*}

**(iii) **A = {*x*:** ***x*** **is a natural number and multiple of 3} = {3, 6, 9 …}** **As B = {*x*: *x* is a natural number less than 6} = {1, 2, 3, 4, 5, 6} A ∪ B = {1, 2, 4, 5, 3, 6, 9, 12 …}

∴ A ∪ B = {*x*: *x* = 1, 2, 4, 5 or a multiple of 3}

**(iv) **A = {*x*:** ***x*** **is a natural number and 1 <** ***x*** **≤ 6} = {2, 3, 4, 5, 6}** **B = {*x*: *x* is a natural number and 6 < *x* < 10} = {7, 8, 9}

A∪ B = {2, 3, 4, 5, 6, 7, 8, 9}

∴ A∪ B = {*x*: *x* ∈ N and 1 < *x* < 10}

**(v) **A = {1, 2, 3}, B = Φ** **A∪ B = {1, 2, 3}

**Question 2:**

Let A = {*a*, *b*}, B = {*a*, *b*, *c*}. Is A ⊂ B? What is A ∪ B?

Answer

Here, A = {*a*, *b*} and B = {*a*, *b*, *c*}

Yes, A ⊂ B.

A∪ B = {*a*, *b*, *c*} = B

**Question 3:**

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

Answer

If A and B are two sets such that A ⊂ B, then A ∪ B = B.

**Question 4:**

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

- A ∪ B
- A ∪ C
- B ∪ C
- B ∪ D
- A ∪ B ∪ C
- A ∪ B ∪ D

**(vii) **B** **∪** **C** **∪** **D

Answer

A = {1, 2, 3, 4], B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}

- A ∪ B = {1, 2, 3, 4, 5, 6}
- A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
- B ∪ C = {3, 4, 5, 6, 7, 8}
- B ∪ D = {3, 4, 5, 6, 7, 8, 9, 10}
- A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8}
- A ∪ B ∪ D = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

**(vii**) B** **∪** **C** **∪** **D = {3, 4, 5, 6, 7, 8, 9, 10}

**Question 5:**

Find the intersection of each pair of sets:

- X = {1, 3, 5} Y = {1, 2, 3}
- A = {
*a*,*e*,*i*,*o*,*u*} B = {*a*,*b*,*c*} - A = {
*x*:*x*is a natural number and multiple of 3} B = {*x*:*x*is a natural number less than 6} - A = {
*x*:*x*is a natural number and 1 <*x*≤ 6}

B = {*x*: *x* is a natural number and 6 < *x* < 10}

**(v) **A = {1, 2, 3}, B = Φ

Answer

- X = {1, 3, 5}, Y = {1, 2, 3} X ∩ Y = {1, 3}
- A = {
*a*,*e*,*i*,*o*,*u*}, B = {*a*,*b*,*c*} A ∩ B = {*a*}- A = {
*x*:*x*is a natural number and multiple of 3} = (3, 6, 9 …} B = {*x*:*x*is a natural number less than 6} = {1, 2, 3, 4, 5}

- A = {

- A ∩ B = {3}
- A = {
*x*:*x*is a natural number and 1 <*x*≤ 6} = {2, 3, 4, 5, 6} B = {*x*:*x*is a natural number and 6 <*x*< 10} = {7, 8, 9}

- A = {

A ∩ B = Φ

- A = {1, 2, 3}, B = Φ

A ∩ B = Φ

**Question 6:**

If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

- A ∩ B
- B ∩ C
- A ∩ C ∩ D
- A ∩ C
- B ∩ D
- A ∩ (B ∪ C)
- A ∩ D
- A ∩ (B ∪ D)
- (A ∩ B) ∩ (B ∪ C)
- (A ∪ D) ∩ (B ∪ C) Answer
- A ∩ B = {7, 9, 11}
- B ∩ C = {11, 13}
- A ∩ C ∩ D = { A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ
- A ∩ C = {11}
- B ∩ D = Φ
- A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

- {7, 9, 11} ∪ {11} = {7, 9, 11}
- A ∩ D = Φ
- A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D)

- {7, 9, 11} ∪ Φ = {7, 9, 11}
- (A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
- (A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15}

- {7, 9, 11, 15}

**Question 7:**

If A = {*x*: *x* is a natural number}, B ={*x*: *x* is an even natural number}

C = {*x*: *x* is an odd natural number} and D = {*x*: *x* is a prime number}, find

- A ∩ B
- A ∩ C
- A ∩ D
- B ∩ C
- B ∩ D
- C ∩ D Answer

A = {*x*: *x* is a natural number} = {1, 2, 3, 4, 5 …}

B ={*x*: *x* is an even natural number} = {2, 4, 6, 8 …} C = {*x*: *x* is an odd natural number} = {1, 3, 5, 7, 9 …}

D = {*x*: *x* is a prime number} = {2, 3, 5, 7 …}

- A ∩B = {
*x*:*x*is a even natural number} = B - A ∩ C = {
*x*:*x*is an odd natural number} = C - A ∩ D = {
*x*:*x*is a prime number} = D - B ∩ C = Φ
- B ∩ D = {2}
- C ∩ D = {
*x*:*x*is odd prime number}

**Question 8:**

Which of the following pairs of sets are disjoint

- {1, 2, 3, 4} and {
*x*:*x*is a natural number and 4 ≤*x*≤ 6} - {
*a*,*e*,*i*,*o*,*u*}and {*c*,*d*,*e*,*f*} - {
*x*:*x*is an even integer} and {*x: x*is an odd integer} Answer- {1, 2, 3, 4}

{*x*: *x* is a natural number and 4 ≤ *x* ≤ *6*} = {4, 5, 6} Now, {1, 2, 3, 4} ∩ {4, 5, 6} = {4}

Therefore, this pair of sets is not disjoint.

**(ii) **{*a*,** ***e*,** ***i*,** ***o*,** ***u*}** **∩** **(*c*,** ***d*,** ***e*,** ***f*} = {*e*}

Therefore, {*a*, *e*, *i*, *o*, *u*} and (*c*, *d*, *e*, *f*} are not disjoint.

**(iii) **{*x*:** ***x*** **is an even integer}** **∩** **{*x*:** ***x*** **is an odd integer} = Φ** **Therefore, this pair of sets is disjoint.

**Question 9:**

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},

C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find

- A – B
- A – C
- A – D
- B – A
- C – A
- D – A
- B – C
- B – D
- C – B
- D – B
- C – D
- D – C Answer
- A – B = {3, 6, 9, 15, 18, 21}
- A – C = {3, 9, 15, 18, 21}

- A – D = {3, 6, 9, 12, 18, 21}
- B – A = {4, 8, 16, 20}
- C – A = {2, 4, 8, 10, 14, 16}
- D – A = {5, 10, 20}
- B – C = {20}
- B – D = {4, 8, 12, 16}
- C – B = {2, 6, 10, 14}
- D – B = {5, 10, 15}
- C – D = {2, 4, 6, 8, 12, 14, 16}
- D – C = {5, 15, 20}

**Question 10:**

If X = {*a*, *b*, *c*, *d*} and Y = {*f*, *b*, *d, g*}, find

- X – Y
- Y – X
- X ∩ Y Answer
- X – Y = {
*a*,*c*} - Y – X = {
*f*,*g*}

- X – Y = {

**(iii) **X** **∩** **Y = {*b*,** ***d*}

**Question 11:**

If **R** is the set of real numbers and **Q** is the set of rational numbers, then what is **R** – **Q**? Answer

R: set of real numbers Q: set of rational numbers

Therefore, R – Q is a set of irrational numbers.

**Question 12:**

State whether each of the following statement is true or false. Justify your answer.

- {2, 3, 4, 5} and {3, 6} are disjoint sets.
- {
*a*,*e*,*i*,*o*,*u*} and {*a*,*b*,*c*,*d*} are disjoint sets. - {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
- {2, 6, 10} and {3, 7, 11} are disjoint sets. Answer
- False

As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6}

⇒ {2, 3, 4, 5} ∩ {3, 6} = {3}

**(ii) **False

As *a* ∈ {*a*, *e*, *i*, *o*, *u*}, *a* ∈ {*a*, *b*, *c*, *d*}

⇒ {*a*, *e*, *i*, *o*, *u* } ∩ {*a*, *b*, *c*, *d*} = {*a*}

**(iii) **True

As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

**(iv) **True

As {2, 6, 10} ∩ {3, 7, 11} = Φ

### NCERT Solutions for Class XI Maths: Chapter 1 – Set

**Exercise 1.1 Solutions****Exercise 1.2 Solutions****Exercise 1.3 Solutions****Exercise 1.4 Solutions****Exercise 1.5 Solutions****Exercise 1.6 Solutions****Miscellaneous Solutions**