Class 11 Maths Chapter 1 Sets – Exercise 1.1 NCERT Solutions

Introduction

Exercise 1.1 introduces the fundamental concepts of sets. A set is a well‑defined collection of distinct objects. You will learn how to represent sets, identify elements, and distinguish between finite, infinite, empty, singleton, and equal sets. This exercise builds the foundation for advanced set operations.

Key Definitions

• Set: A collection of distinct objects.

• Element: Each object in a set.

• Empty Set ($\mathrm{\varnothing }$): A set with no elements.

• Finite Set: A set with countable elements.

• Infinite Set: A set with uncountable elements.

• Singleton Set: A set with exactly one element.

• Equal Sets: Two sets with exactly the same elements.

• Subset: If every element of $A$ is in $B$, then $A\subseteq B$.

NCERT Questions with Solutions (10)

Q1. Which of the following are sets? Justify. Examples: collection of vowels in English alphabet, collection of good students in a class.

• Vowels = $\{a,e,i,o,u\}$ → well‑defined, hence a set.

• Good students = subjective, not well‑defined, hence not a set.

Q2. Write sets for following statements. (i) Odd natural numbers less than 10.

$$A=\{1,3,5,7,9\}$$

(ii) Letters of word "MATH".

$$B=\{M,A,T,H\}$$

Q3. State whether following sets are finite or infinite. (i) Set of natural numbers less than 100 → finite. (ii) Set of prime numbers → infinite.

Q4. Write empty set examples. (i) Set of even prime numbers greater than 2 → $\mathrm{\varnothing }$. (ii) Set of natural numbers less than 1 → $\mathrm{\varnothing }$.

Q5. Write singleton set examples. (i) $\{0\}$, (ii) $\{5\}$.

Q6. Write equal sets examples. $\{1,2,3\}$ and $\{3,2,1\}$ are equal sets.

Q7. Write subset examples. If $A=\{1,2\}$, $B=\{1,2,3\}$, then $A\subseteq B$.

Q8. Write universal set example. For natural numbers less than 10, universal set $U=\{1,2,3,4,5,6,7,8,9\}$.

Q9. Write infinite set examples. (i) Set of natural numbers. (ii) Set of integers.

Q10. Write finite set examples. (i) Set of months in a year. (ii) Set of letters in word "ALGEBRA".

FAQs (10)

1. What is a set? A well‑defined collection of distinct objects.

2. What is empty set? A set with no elements.

3. What is finite set? A set with countable elements.

4. What is infinite set? A set with uncountable elements.

5. What is singleton set? A set with exactly one element.

6. What are equal sets? Sets with exactly same elements.

7. What is subset? If every element of $A$ is in $B$, then $A\subseteq B$.

8. What is universal set? A set containing all elements under consideration.

9. What is cardinality of set? Number of elements in set.

10. Why is this exercise important? It builds foundation for operations on sets.

Conclusion

Exercise 1.1 has 10 solved questions and 10 FAQs that strengthen your understanding of basic set theory. This builds the foundation for advanced topics in Class 11 Maths.

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