NCERT Solutions Class 11 Maths Chapter 1 – Sets
NCERT Solutions for Class 11 Maths Chapter 1: Sets
Sets form the foundation of modern mathematics. This chapter introduces set notation, types of sets, set operations, and Venn diagrams. Understanding sets is crucial for functions, relations, probability, and all higher mathematics.
Exercise 1.1 Solutions
Q1. Which of the following are sets? Justify your answer.
(i) The collection of all 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.
Answer:
- (i) Set – Well-defined collection: {January, June, July}
- (ii) Not a set – “Most talented” is subjective, not well-defined
- (iii) Not a set – “Best” is subjective, different people have different opinions
Q2. 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}
Answer:
- (i) A = {–3, –2, –1, 0, 1, 2, 3, 4, 5, 6}
- (ii) B = {1, 2, 3, 4, 5}
Exercise 1.2 Solutions
Q1. Which of the following are examples of empty set?
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
Answer:
- (i) Empty set (∅) – No odd number is divisible by 2
- (ii) Not empty – {2} is the only even prime number
Q2. State whether each of the following set is finite or infinite:
(i) The set of lines parallel to the x-axis
(ii) The set of circles passing through the origin (0, 0)
Answer:
- (i) Infinite – There are infinitely many lines parallel to x-axis (y = c for any real c)
- (ii) Infinite – Infinitely many circles can pass through the origin
Exercise 1.4 Solutions
Q1. Find the union of each of the following pairs of sets:
(i) A = {1, 3, 5}, B = {1, 2, 3}
(ii) A = {a, e, i, o, u}, B = {a, b, c}
Answer:
- (i) A ∪ B = {1, 2, 3, 5}
- (ii) A ∪ B = {a, b, c, e, i, o, u}
Q2. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15}, find:
(i) A ∩ (B ∪ C) (ii) (A ∩ B) ∩ (B ∪ C)
Solution:
(i) B ∪ C = {7, 9, 11, 13, 15}
A ∩ (B ∪ C) = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
(ii) A ∩ B = {7, 9, 11}
B ∪ C = {7, 9, 11, 13, 15}
(A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}
Important Set Formulas
| Property | Formula |
|---|---|
| Cardinal number (2 sets) | n(A ∪ B) = n(A) + n(B) – n(A ∩ B) |
| Cardinal number (3 sets) | n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C) |
| De Morgan’s Laws | (A ∪ B)’ = A’ ∩ B’ and (A ∩ B)’ = A’ ∪ B’ |
| Power Set | n(P(A)) = 2ⁿ where n = n(A) |
Key Takeaways
- A set is a well-defined collection of distinct objects
- Sets can be represented in roster form or set-builder form
- Empty set (∅) has no elements; Universal set (U) contains all elements
- A ⊂ B means A is a subset of B
- Power set of A contains all subsets including ∅ and A itself
- Union (∪), intersection (∩), and complement (‘) are basic operations
- Venn diagrams help visualize set relationships
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