NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3 PDF

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3: Chapter 1 of Class 11 Maths, Sets , introduces fundamental concepts of set theory. Exercise 1.3 focuses on operations on sets, including union, intersection, difference, and complement of sets. It emphasizes understanding Venn diagrams for visual representation and solving practical problems involving these operations.

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3 Overview

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3 PDF

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3 PDF

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3 Question Answers

1. 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}

Solution:

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}

Solution:

3. Let A = {1, 2, {3, 4}, 5}. Which of the following statements is 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

Solution:

4. Write down all the subsets of the following sets:

(i) { a }

(ii) { a , b }

(iii) {1, 2, 3}

(iv) Φ

Solution:

5. How many elements has P (A), if A = Φ?

Solution:

6. 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}

Solution:

7. Write the following intervals in set-builder form:

(i) (–3, 0)

(ii) [6, 12]

(iii) (6, 12]

(iv) [–23, 5)

Solution:

8. What universal set (s) would you propose for each of the following?

(i) The set of right triangles

(ii) The set of isosceles triangles

Solution:

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 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:

Benefits of Using NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3

Step-by-Step Solutions : Provides clear, detailed explanations for understanding complex set operations like union, intersection, and complement.

Time-Saving : Offers accurate answers to quickly verify solutions and improve efficiency in problem-solving.

Concept Clarity : Strengthens foundational knowledge of set theory, which is crucial for advanced topics like relations, probability, and calculus.

Exam Preparation : Helps identify important problem types frequently asked in exams.

Error-Free Learning : Minimizes mistakes through well-structured and error-free answers, boosting confidence.

Visual Learning : Enhances understanding using Venn diagrams for practical applications.

Accessibility : Easy to download and refer to, ensuring effective self-study anytime.