The NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.2 have been prepared by the subject experts at BYJU’S and are in accordance with the latest CBSE Syllabus 2023-24. Exercise 1.2 of NCERT Solutions for Class 11 Maths Chapter 1 – Sets are based on the following topics:
- The Empty Set: A set which does not contain any element is called the empty set or the null set, or the void set.
- Finite and Infinite Sets: A set which is empty or consists of a definite number of elements is called finite; otherwise, the set is called infinite
- Equal Sets: Two sets, A and B, are said to be equal if they have exactly the same elements, and we write A = B. Otherwise, the sets are said to be unequal, and we write A ≠B
The subject specialists stick to the latest CBSE syllabus while preparing the solutions. The problem-solving method provided in the examples is followed while preparing the NCERT Solutions for Class 11 as well.
NCERT Solutions for Class 11 Maths Chapter 1 – Sets Exercise 1.2
Class 11 Maths Chapter 1- Sets exercise 1.2 Solutions
1. Which of the following are examples of the null set?
(i) Set of odd natural numbers divisible by 2
(ii) Set of even prime numbers
(iii) {x: x is a natural numbers, x < 5 and x > 7}
(iv) {y: y is a point common to any two parallel lines}
Solution:
(i) Set of odd natural numbers divisible by 2 is a null set, as odd numbers are not divisible by 2.
(ii) Set of even prime numbers is not a null set, as 2 is an even prime number.
(iii) {x: x is a natural number, x < 5 and x > 7} is a null set, as a number cannot be both less than 5 and greater than 7.
(iv)Â {y:Â y is a point common to any two parallel lines} is a null set, as the parallel lines do not intersect. Therefore, they have no common point.
2. Which of the following sets are finite or infinite?
(i) The set of months of a year
(ii) {1, 2, 3 …}
(iii) {1, 2, 3 … 99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less than 99
Solution:
(i) The set of months of a year is a finite set, as it contains 12 elements.
(ii) {1, 2, 3 …} is an infinite set because it has an infinite number of natural numbers.
(iii) {1, 2, 3 …99, 100} is a finite set, as the numbers from 1 to 100 are finite.
(iv) The set of positive integers greater than 100 is an infinite set, as the positive integers, which are greater than 100, are infinite.
(v) The set of prime numbers less than 99 is a finite set, as the prime numbers which are less than 99 are finite.
3. State whether each of the following sets is finite or infinite.
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)
Solution:
(i) The set of lines which are parallel to the x-axis is an infinite set, as the lines which are parallel to the x-axis are infinite.
(ii) The set of letters in the English alphabet is a finite set, as it contains 26 elements.
(iii) The set of numbers which are multiple of 5 is an infinite set, as the multiples of 5 are infinite.
(iv) The set of animals living on the earth is a finite set, as the number of animals living on the earth is finite.
(v) The set of circles passing through the origin (0, 0) is an infinite set, as an infinite number of circles can pass through the origin.
4. In the following, state whether A = B or not.
(i) A = {a, b, c, d}; B = {d, c, b, a}
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10}
(iv) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30 …}
Solution:
(i) A = {a, b, c, d}; B = {d, c, b, a}
The order in which the elements of a set are listed is not significant.
Therefore, A = B.
(ii)Â A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
We know that 12 ∈ A but 12 ∉ B.
Therefore, A ≠B
(iii)Â A = {2, 4, 6, 8, 10};
B = {x: x is a positive even integer and x ≤ 10} = {2, 4, 6, 8, 10}
Therefore, A = B
(iv) A = {x: x is a multiple of 10}
B = {10, 15, 20, 25, 30 …}
We know that 15 ∈ B but 15 ∉ A.
Therefore, A ≠B
5. Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0}
(ii) A = {x: x is a letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
Solution:
(i) A = {2, 3}; B = {x: x is solution of x2 + 5x + 6 = 0}
x2 + 5x + 6 = 0 can be written as
x(x + 3) + 2(x + 3) = 0
By further calculation,
(x + 2) (x + 3) = 0
So, we get
x = –2 or x = –3
Here,
A = {2, 3}; B = {–2, –3}
Therefore, A ≠B
(ii) A = {x: x is a letter in the word FOLLOW} = {F, O, L, W}
B = {y: y is a letter in the word WOLF} = {W, O, L, F}
The order in which the elements of a set which are listed is not significant.
Therefore, A = B.
6. From the sets given below, select equal sets.
A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}
E = {–1, 1}, F = {0, a}, G = {1, –1}, H = {0, 1}
Solution:
A = {2, 4, 8, 12}; B = {1, 2, 3, 4}; C = {4, 8, 12, 14}
D = {3, 1, 4, 2}; E = {–1, 1}; F = {0, a}
G = {1, –1}; H = {0, 1}
We know that
8 ∈ A, 8 ∉ B, 8 ∉ D, 8 ∉ E, 8 ∉ F, 8 ∉ G, 8 ∉ H
A ≠B, A ≠D, A ≠E, A ≠F, A ≠G, A ≠H
It can be written as
2 ∈ A, 2 ∉ C
Therefore, A ≠C
3 ∈ B, 3 ∉ C, 3 ∉ E, 3 ∉ F, 3 ∉ G, 3 ∉ H
B ≠C, B ≠E, B ≠F, B ≠G, B ≠H
It can be written as
12 ∈ C, 12 ∉ D, 12 ∉ E, 12 ∉ F, 12 ∉ G, 12 ∉ H
Therefore, C ≠D, C ≠E, C ≠F, C ≠G, C ≠H
4 ∈ D, 4 ∉ E, 4 ∉ F, 4 ∉ G, 4 ∉ H
Therefore, D ≠E, D ≠F, D ≠G, D ≠H
Here, E ≠F, E ≠G, E ≠H
F ≠G, F ≠H, G ≠H
The order in which the elements of a set are listed is not significant.
B = D and E = G
Therefore, among the given sets, B = D and E = G.
Access other exercise solutions of Class 11 Maths Chapter 1 – Sets
The other exercises of NCERT Class 11 Maths Solutions for Chapter 1 are as follows.
Exercise 1.1 Solutions 6 Questions
Exercise 1.3 Solutions 9 Questions
Exercise 1.4 Solutions 12 Questions
Exercise 1.5 Solutions 7 Questions
Exercise 1.6 Solutions 8 Questions
Miscellaneous Exercise on Chapter 1 Solutions 16 Questions
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