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 1.3**

**Question 1:**

Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:

- {2, 3, 4} … {1, 2, 3, 4, 5}
- {
*a*,*b*,*c*} … {*b*,*c*,*d*} - {
*x*:*x*is a student of Class XI of your school} … {*x*:*x*student of your school} - {
*x*:*x*is a circle in the plane} … {*x*:*x*is a circle in the same plane with radius 1 unit} - {
*x*:*x*is a triangle in a plane}…{*x*:*x*is a rectangle in the plane} - {
*x*:*x*is an equilateral triangle in a plane}… {*x*:*x*is a triangle in the same plane} - {
*x*:*x*is an even natural number} … {*x*:*x*is an integer}

Answer

**(i) **

**(ii) **

- {
*x*:*x*is a student of class XI of your school}⊂ {*x*:*x*is student of your school} - {
*x*:*x*is a circle in the plane} ⊄ {*x*:*x*is a circle in the same plane with radius 1 unit} - {
*x*:*x*is a triangle in a plane} ⊄ {*x*:*x*is a rectangle in the plane} - {
*x*:*x*is an equilateral triangle in a plane}⊂ {*x*:*x*in a triangle in the same plane}

**(vii) **{*x*:** ***x*** **is an even natural number}** **⊂** **{*x*:** ***x*** **is an integer}

**Question 2:**

Examine whether the following statements are true or false:

- {
*a*,*b*} ⊄ {*b*,*c*,*a*} - {
*a*,*e*} ⊂ {*x*:*x*is a vowel in the English alphabet} - {1, 2, 3} ⊂{1, 3, 5}
- {
*a*} ⊂ {*a*.*b*,*c*} - {
*a*} ∈ (*a*,*b*,*c*) - {
*x*:*x*is an even natural number less than 6} ⊂ {*x*:*x*is a natural number which divides 36}

Answer

- False. Each element of {
*a*,*b*} is also an element of {*b*,*c*,*a*}. - True.
*a*,*e*are two vowels of the English alphabet.

- False. Each element of {

- False. 2∈{1, 2, 3}; however, 2∉{1, 3, 5}
- True. Each element of {
*a*} is also an element of {*a*,*b*,*c*}. - False. The elements of {
*a*,*b*,*c*} are*a*,*b*,*c*. Therefore, {*a*}⊂{*a*,*b*,*c*} - True. {
*x*:*x*is an even natural number less than 6} = {2, 4}

{*x*:*x* is a natural number which divides 36}= {1, 2, 3, 4, 6, 9, 12, 18, 36}

**Question 3:**

Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why?

- {3, 4}⊂ A
- {3, 4}}∈ A
- {{3, 4}}⊂ A
- 1∈ A
- 1⊂ A
- {1, 2, 5} ⊂ A
- {1, 2, 5} ∈ A
- {1, 2, 3} ⊂ A
- Φ ∈ A
- Φ ⊂ A

**(xi) **{Φ}** **⊂** **A

Answer

A = {1, 2, {3, 4}, 5}

The statement {3, 4} ⊂ A is incorrect because 3 ∈ {3, 4}; however, 3∉A.

The statement {3, 4} ∈A is correct because {3, 4} is an element of A.

The statement {{3, 4}} ⊂ A is correct because {3, 4} ∈ {{3, 4}} and {3, 4} ∈ A.

The statement 1∈A is correct because 1 is an element of A.

The statement 1⊂ A is incorrect because an element of a set can never be a subset of itself.

The statement {1, 2, 5} ⊂ A is correct because each element of {1, 2, 5} is also an element of A.

The statement {1, 2, 5} ∈ A is incorrect because {1, 2, 5} is not an element of A.

**(viii**) The statement {1, 2, 3}** **⊂** **A is incorrect because 3** **∈** **{1, 2, 3}; however, 3** **∉** **A.

The statement Φ ∈ A is incorrect because Φ is not an element of A.

The statement Φ ⊂ A is correct because Φ is a subset of every set.

The statement {Φ} ⊂ A is incorrect because Φ∈ {Φ}; however, Φ ∈ A.

**Question 4:**

Write down all the subsets of the following sets:

- {
*a*} - {
*a*,*b*} - {1, 2, 3}
- Φ

Answer

- The subsets of {
*a*} are Φ and {*a*}. - The subsets of {
*a*,*b*} areΦ, {*a*}, {*b*}, and {*a*,*b*}.- The subsets of {1, 2, 3} areΦ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and {1, 2, 3}
- The only subset of Φ isΦ.

**Question 5:**

How many elements has P(A), if A = Φ?

Answer

We know that if A is a set with *m* elements i.e., *n*(A) = *m*, then *n*[P(A)] = 2* ^{m}*. If A = Φ, then

*n*(A) = 0.

∴ *n*[P(A)] = 2^{} = 1

Hence, P(A) has one element.

**Question 6:**

Write the following as intervals:

- {
*x*:*x*∈ R, –4 <*x*≤ 6} - {
*x*:*x*∈ R, –12 <*x*< –10} - {
*x*:*x*∈ R, 0 ≤*x*< 7} - {
*x*:*x*∈ R, 3 ≤*x*≤ 4} Answer- {
*x*:*x*∈ R, –4 <*x*≤ 6} = (–4, 6] - {
*x*:*x*∈ R, –12 <*x*< –10} = (–12, –10)

- {
- {
*x*:*x*∈ R, 0 ≤*x*< 7} = [0, 7) - {
*x*:*x*∈ R, 3 ≤*x*≤ 4} = [3, 4]

**Question 7:**

Write the following intervals in set-builder form:

- (–3, 0)
- [6, 12]
- (6, 12]
- [–23, 5) Answer
- (–3, 0) = {
*x*:*x*∈ R, –3 <*x*< 0} - [6, 12] = {
*x*:*x*∈ R, 6 ≤*x*≤ 12}

- (–3, 0) = {
- (6, 12] ={
*x*:*x*∈ R, 6 <*x*≤ 12} - [–23, 5) = {
*x*:*x*∈ R, –23 ≤*x*< 5}

**Question 8:**

What universal set (s) would you propose for each of the following:

- The set of right triangles
- The set of isosceles triangles Answer
- For the set of right triangles, the universal set can be the set of triangles or the set of polygons.
- For the set of isosceles triangles, the universal set can be the set of triangles or the set of polygons or the set of two-dimensional figures.

**Question 9:**

Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals set (s) for all the three sets A, B and C

- {0, 1, 2, 3, 4, 5, 6}
- Φ
- {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- {1, 2, 3, 4, 5, 6, 7, 8}

Answer

- It can be seen that A ⊂ {0, 1, 2, 3, 4, 5, 6} B ⊂ {0, 1, 2, 3, 4, 5, 6}

However, C ⊄ {0, 1, 2, 3, 4, 5, 6}

Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C.

- A ⊄ Φ, B ⊄ Φ, C ⊄ Φ

Therefore, Φ cannot be the universal set for the sets A, B, and C.

- A ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

C ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Therefore, the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the sets A, B, and C.

- A ⊂ {1, 2, 3, 4, 5, 6, 7, 8}

B ⊂ {1, 2, 3, 4, 5, 6, 7, 8}

However, C ⊄ {1, 2, 3, 4, 5, 6, 7, 8}

Therefore, the set {1, 2, 3, 4, 5, 6, 7, 8} cannot be the universal set for the sets A, B, and C.

### 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**