Our ncert solutions for Exercise 1.3 Class 11 maths 1. Sets - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

# Exercise 1.3 Class 11 maths 1. Sets - ncert solutions - Toppers Study

Topper Study classes prepares ncert solutions on practical base problems and comes out with the best result that helps the students and teachers as well as tutors and so many ecademic coaching classes that they need in practical life. Our ncert solutions for Exercise 1.3 Class 11 maths 1. Sets - ncert solutions - Toppers Study is the best material for English Medium students cbse board and other state boards students.

## Exercise 1.3 Class 11 maths 1. Sets - ncert solutions - Toppers Study

CBSE board students who preparing for **class 11 ncert solutions maths and Mathematics** solved exercise **chapter 1. Sets** available and this helps in upcoming exams
2024-2025.

### You can Find Mathematics solution Class 11 Chapter 1. Sets

- All Chapter review quick revision notes for chapter 1. Sets Class 11
- NCERT Solutions And Textual questions Answers Class 11 Mathematics
- Extra NCERT Book questions Answers Class 11 Mathematics
- Importatnt key points with additional Assignment and questions bank solved.

NCERT Solutions do not only help you to cover your syllabus but also will give to textual support in exams 2024-2025 to complete **exercise 1.3 maths class 11 chapter 1** in english medium. So revise and practice these all cbse study materials like class 11 maths chapter 1.3 in english ncert book. Also ensure to repractice all syllabus within time or before board exams for ncert class 11 maths ex 1.3 in english.

See all solutions for class 11 maths chapter 1 exercise 1 in english medium solved questions with answers.

### Exercise 1.3 class 11 Mathematics Chapter 1. Sets

Sure! The following topics will be covered in this article

- Exercise 1.3 Class 11 Maths 1. Sets - Ncert Solutions - Toppers Study
- Class 11 Ncert Solutions
- Solution Chapter 1. Sets Class 11
- Solutions Class 11
- Chapter 1. Sets Exercise 1.3 Class 11

**Notice**: Undefined offset: 5 in

**/home/atpeduca/public_html/toppersstudy.com/view-home.php**on line

**123**

## 1. Sets

### | Exercise 1.3 |

## Exercise 1.3 Class 11 maths 1. Sets - ncert solutions - Toppers Study

**Exercise 1.3 **

**Q1. Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :
(i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 } **

**(ii) { a, b, c } . . . { b, c, d }
(iii) {x : x is a student of Class XI of your school}. . .{x : x student of your school}
(iv) {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with
radius 1 unit}
(v) {x : x is a triangle in a plane} . . . {x : x is a rectangle in the plane}
(vi) {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane}
(vii) {x : x is an even natural number} . . . {x : x is an integer}**

**Solutions: **

(i) { 2, 3, 4 } ⊂ { 1, 2, 3, 4,5 }

(ii) { a, b, c } ⊄ { b, c, d }

(iii) {x : x is a student of Class XI of your school} ⊂ {x : x student of your school}

(iv) {x : x is a circle in the plane} ⊄ {x : x is a circle in the same plane with radius 1 unit}

(v) {x : x is a triangle in a plane} ⊄ {x : x is a rectangle in the plane}

(vi) {x : x is an equilateral triangle in a plane} ⊂ {x : x is a triangle in the same plane}

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

**2. Examine whether the following statements are true or false:
(i) { a, b } ⊄ { b, c, a }
(ii) { a, e } ⊂ { x : x is a vowel in the English alphabet}
(iii) { 1, 2, 3 } ⊂ { 1, 3, 5 }
(iv) { a }⊂ { a, b, c }
(v) { a }∈ { a, b, c }
(vi) { x : x is an even natural number less than 6} ⊂ { x : x is a natural number which divides 36}**

**Solutions: **

(i) **False**, Because Each element of { a, b } is also an element of { b, c, a }.

(ii) **True**, Because {a, e} is also vowels of English alphabet.

(iii) **False**, Hence 2 ∈ {1, 2, 3}; while, 2 ∉ {1, 3, 5}

(iv) True, Because each elements of set { a } is also element of { a, b, c }

**Q3. Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
(i) {3, 4} ⊂ A **

**(ii) {3, 4} ∈ A **

**(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A (v) 1 ⊂ A **

**(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A **

**(viii) {1, 2, 3} ⊂ A **

**(ix) φ ∈ A
(x) φ ⊂ A **

**(xi) {φ} ⊂ A**

**Solutions:**

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

(i) The statement {3, 4} ⊂ A is incorrect because 3 ∈ {3, 4}; while, 3∉A.

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

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

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

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

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

(vii)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.

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

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

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

**Q4. Write down all the subsets of the following sets
(i) {a} (ii) {a, b} (iii) {1, 2, 3} (iv) φ**

**Solutions: **

(i) The subsets of {a} are φ and {a}.

(ii) The subsets of {a, b} are φ, {a}, {b} and {a, b}.

(iii) The subsets of {1, 2, 3} are φ, {1}, {2}, {3}, {1, 2}, {1,3}, {2, 3} and {1, 2, 3}.

(iv) The subset of φ is φ.

**Q5. How many elements has P(A), if A = φ?**

**Solution: **

Given that A = φ

Therefore, no. of elements n(A) = 0

n[P(A)] = 2^{n} = 2^{0} = 1

Hence, P(A) has only 1 element.

**Q6. Write the following as intervals :
(i) {x : x ∈ R, – 4 < x ≤ 6} **

**(ii) {x : x ∈ R, – 12 < x < –10}
(iii) {x : x ∈ R, 0 ≤ x < 7} **

**(iv) {x : x ∈ R, 3 ≤ x ≤ 4}**

**Solutions: **

(i) {x: x ∈ R, –4 < x ≤ 6} is an open interval from -4 to 6, including 6 but excluding -4.

Hence interval = (–4, 6]

(ii) {x: x ∈ R, –12 < x < –10} is an open interval from -12 to -10, excluding both -12 and -10.

Hence interval = (–12, –10)

(iii) {x: x ∈ R, 0 ≤ x < 7} is an open interval from 0 to 7, including 0 but excluding 7.

Hence interval = [0, 7)

(iv) {x: x ∈ R, 3 ≤ x ≤ 4} is an close interval from 3 to 4, including both 3 and 4.

Hence interval = [3, 4]

**Q7. Write the following intervals in set-builder form :
(i) (– 3, 0) **

**(ii) [6 , 12] **

**(iii) (6, 12] **

**(iv) [–23, 5)**

**Solutions: **

(i) (–3, 0) = {x: x ∈ R, –3 < x < 0}

(ii) [6, 12] = {x: x ∈ R, 6 ≤ x ≤ 12}

(iii) (6, 12] = {x: x ∈ R, 6 < x ≤ 12}

(iv) [–23, 5) = {x: x ∈ R, –23 ≤ x < 5}

**Q8. What universal set(s) would you propose for each of the following :
(i) The set of right triangles. **

**(ii) The set of isosceles triangles.**

**Solutions: **

(i) The sets of all possible triangles and polygons can be universal set for the right triangles.

(ii) The sets of all possible triangles and polygons can be universal set for the isosceles triangles.

**Q9. 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 universal set (s) for all the three sets A, B and C
(i) {0, 1, 2, 3, 4, 5, 6}
(ii) φ
(iii) {0,1,2,3,4,5,6,7,8,9,10}
(iv) {1,2,3,4,5,6,7,8}**

**Solution: **

(iii) {0,1,2,3,4,5,6,7,8,9,10} can be universal set (s) for all the three sets A, B and C.

Because,

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.

##### Other Pages of this Chapter: 1. Sets

### Select Your CBSE Classes

Important Study materials for classes 06, 07, 08,09,10, 11 and 12. Like CBSE Notes, Notes for Science, Notes for maths, Notes for Social Science, Notes for Accountancy, Notes for Economics, Notes for political Science, Noes for History, Notes For Bussiness Study, Physical Educations, Sample Papers, Test Papers, Mock Test Papers, Support Materials and Books.

*Mathematics Class - 11th*

NCERT Maths book for CBSE Students.

books

## Study Materials List:

##### Solutions ⇒ Class 11th ⇒ Mathematics

## Topper's Study

New Books