NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.1 Sets help students understand the basic concepts of Sets in a clear and exam-oriented manner. This exercise introduces students to the fundamental idea of sets and how to represent them using different methods.
Prepared according to the latest CBSE Class 11 Maths syllabus, Exercise 1.1 focuses on identifying sets, writing sets in roster form and set-builder form, and understanding different types of sets. Regular practice of this exercise helps students build a strong foundation for advanced topics in mathematics.
NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.1
Q.
Which of the following are sets ? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of India.
(iii) A team of eleven best-cricket batsmen of the world.
(iv) The collection of all boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of most dangerous animals of the world.
Q.
Let A = 1, 2, 3, 4, 5, 6. Insert the appropriate symbol ∈or ∈/in the blank spaces:(i) 5 . . . A (ii) 8 . . . A (iii) 0 . . . A(iv) 4 . . . A (v) 2 . . . A (vi) 10 . . . A
Q.
Write the following sets in roster form:
(i) A = {x: x is an integer and –3 < x < 7}
(ii) B = {x: x is a natural number less than 6}
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}
(v) E = The set of all letters in the word TRIGONOMETRY
(vi) F = The set of all letters in the word BETTER
Q.
Write the following sets in the set-builder form:
(i) (3, 6, 9, 12}
(ii) {2, 4, 8,16,32}
(iii) {5, 25, 125, 625}
(iv) {2, 4, 6, . . .}
(v) {1,4,9, . . .,100}
The solutions are explained in a clear, step-by-step manner so students can easily understand the concept of sets, their representation, and their applications in mathematical problems.
Q1. Which of the following are sets? Justify your answer.
(i) The collection of all months of a year beginning with the letter J.
Solution: This is a set because it is a collection of well-defined objects. We can clearly identify the months as January, June, and July.
(ii) The collection of ten most talented writers of India.
Solution: This is not a set because the criteria for "most talented" is subjective and varies from person to person
(iii) A team of eleven best cricket batsmen of the world.
Solution: This is not a set because the term "best" is subjective and not well-defined.
(iv) The collection of all boys in your class.
Solution: This is a set because the boys in a specific class can be clearly identified.
(v) The collection of all natural numbers less than 100.
Solution: This is a set because these numbers $(1, 2, 3, \dots, 99)$ are clearly defined.
(vi) A collection of novels written by Munshi Premchand.
Solution: This is a set because the list of novels written by this specific author is fixed and identifiable.
(vii) The collection of all even integers.
Solution: This is a set because even integers $(2, 4, 6, \dots)$ are well-defined.
(viii) The collection of questions in this chapter.
Solution: This is a set because all questions within the chapter are clearly identifiable.
(ix) A collection of the most dangerous animals in the world.
Solution: This is not a set because the definition of "most dangerous" is subjective and varies.
Q2. Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ (belongs to) or $\notin$ (does not belong to) in the blank spaces:
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(i) $5 \in A$ (Since 5 is an element of the set)
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(ii) $8 \notin A$ (Since 8 is not in the set)
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(iii) $0 \notin A$ (Since 0 is not in the set)
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(iv) $4 \in A$ (Since 4 is an element of the set)
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(v) $2 \in A$ (Since 2 is an element of the set)
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(vi) $10 \notin A$ (Since 10 is not in the set)
Q3. Write the following sets in roster form.
(i) $A = \{x : x \text{ is an integer and } -3 < x < 7\}$
Solution: $A = \{-2, -1, 0, 1, 2, 3, 4, 5, 6\}$
(ii) $B = \{x : x \text{ is a natural number less than 6}\}$
Solution: $B = \{1, 2, 3, 4, 5\}$
(iii) $C = \{x : x \text{ is a two-digit number such that sum of digits is 8}\}$
Solution: $C = \{17, 26, 35, 44, 53, 62, 71, 80\}$
(iv) $D = \{x : x \text{ is a prime number and divisor of 60}\}$
Solution: The prime divisors of 60 are 2, 3, and 5. So, $D = \{2, 3, 5\}$
(v) $E = \text{The set of all letters in the word TRIGONOMETRY}$
Solution: $E = \{T, R, I, G, O, N, M, E, Y\}$ (Note: Letters are not repeated in a set).
(vi) $F = \text{The set of all letters in the word BETTER}$
Solution: $F = \{B, E, T, R\}$
FAQs – Class 11 Maths Chapter 1 Exercise 1.1 Sets
Q1. What is the focus of Exercise 1.1?
Exercise 1.1 focuses on understanding the basic definition of sets, methods of representing sets, and identifying elements of a set.
Q2. What are the different ways to represent a set?
Sets can be represented mainly in two ways:
Q3. Why is Exercise 1.1 important for Class 11 Maths?
This exercise builds the foundation for the entire chapter on Sets, which is used in many advanced mathematical topics like relations, functions, and probability.
Q4. How can students prepare effectively for Exercise 1.1?
Students should understand the definition of sets clearly, practice writing sets in both forms, and solve multiple examples to strengthen their concepts.