Class 11 Sets NCERT solution|NCERT Solutions for Class 11 Maths Chapter 1 Sets| Sets class 11 1.1 exercise solutions|VECTOR STUDIES
NCERT Solutions for Class 11 Maths Chapter 1- Sets
exercise 1.1
Q1. Which of the following are sets? Justify our 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.
(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.
Solution:
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects and distinct. Therefore, this collection is a set.
(ii) The collection of ten most talented writers of India is not a well-defined collection as the criteria to determine a writer’s talent may differ from one person to another.Therefore, this collection is not a set.
(iii) A team of eleven best-cricket batsmen of the world is not a well-defined collection as the criteria to determine a batsman’s talent, it may vary from one person to another.Therefore, this collection is not a set.
(iv) The collection of all boys in your class is a well-defined and distinct collection as you can identify a boy who belongs to this collection.Therefore, this collection is a set.
(v) The collection of all natural numbers less than 100 is a well-defined collection as one can find a number which belongs to this collection.Therefore, this collection is a set.
(vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined and distinct collection.Therefore, this collection is a set.
(vii) The collection of all even integers is a well-defined collection as one can find an integer which belongs to this collection.Therefore, this collection is a set.
(viii) The collection of questions in this Chapter is a well-defined collection as one can find a question which belongs to this chapter.Therefore, this collection is a set.
(ix) A collection of most dangerous animals of the world is not a well-defined collection as the criteria to find the dangerousness of an animal can vary from one animal to another.Therefore, this collection is not a set.
Q2. 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
Solution:
(i) 5 ∈ A
(ii) 8 ∉ A
(iii) 0 ∉ A
(iv) 4 ∈ A
(v) 2 ∈ A
(vi) 10 ∉ A
Q3. 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.
Solution:
(i) A = {x: x is an integer and –3 < x < 7} =
–2, –1, 0, 1, 2, 3, 4, 5, and 6 only are the elements of this set.
Hence, the given set can be written in roster form as
A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {x: x is a natural number less than 6}
1, 2, 3, 4, and 5 only are the elements of this set
Hence, the given set can be written in roster form as
B = {1, 2, 3, 4, 5}
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
17, 26, 35, 44, 53, 62, 71, and 80 only are the elements of this set
Hence, the given set can be written in roster form as
C = {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = {x: x is a prime number which is divisor of 60}
Here 60 = 2 × 2 × 3 × 5
2, 3 and 5 only are the elements of this set
Hence, the given set can be written in roaster form as
D = {2, 3, 5}
(v) E = The set of all letters in the word TRIGONOMETRY
TRIGONOMETRY is a 12 letters word out of which T, R and O are repeated.
Hence, the given set can be written in roaster form as
E = {T, R, I, G, O, N, M, E, Y}
(vi) F = The set of all letters in the word BETTER
BETTER is a 6 letters word out of which E and T are repeated.
Hence, the given set can be written in roaster form as
F = {B, E, T, R}
Q4. 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}
Solution:
i) {3, 6, 9, 12}
The given set can be written in the set-builder form as {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32}
We know that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25
Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}.
(iii) {5, 25, 125, 625}
We know that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.
Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as {x: x = 5n, n ∈N and 1 ≤ n ≤ 4}.
(iv) {2, 4, 6 …}
{2, 4, 6 …} is a set of all even natural numbers
Therefore, the given set {2, 4, 6 …} can be written in the set-builder form as {x: x is an even natural number}.
(v) {1, 4, 9 … 100}
We know that 1 = 12, 4 = 22, 9 = 32 …100 = 102.
Therefore, the given set {1, 4, 9… 100} can be written in the set-builder form as {x: x = n2, n ∈ N and 1 ≤ n ≤ 10}.
Q5. List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
(ii) B = {x: x is an integer, -1/2 < x < 9/2}
(iii) C = {x: x is an integer, x2 ≤ 4}
(iv) D = {x: x is a letter in the word “LOYAL”}
(v) E = {x: x is a month of a year not having 31 days}
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.
Solution:
(i) A = {x: x is an odd natural number}
So, the elements are A = {1, 3, 5, 7, 9 …..}
(ii) B = {x: x is an integer, -1/2 < x < 9/2}
We know that – 1/2 = – 0.5 and 9/2 = 4.5
So the elements are B = {0, 1, 2, 3, 4}.
(iii) C = {x: x is an integer, x2 ≤ 4}
We know that
(–1)2 = 1 ≤ 4; (–2)2 = 4 ≤ 4; (–3)2 = 9 > 4
Here
02 = 0 ≤ 4, 12 = 1 ≤ 4, 22 = 4 ≤ 4, 32 = 9 > 4
So, we get
C = {–2, –1, 0, 1, 2}
(iv) D = {x: x is a letter in the word “LOYAL”}
So ,the elements are D = {L, O, Y, A}
(v) E = {x: x is a month of a year not having 31 days}
So, the elements are E = {February, April, June, September, November}
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}
So, the elements are F = {b, c, d, f, g, h, j}
For notes of this chapter visit-https://vectorstudiesindia.blogspot.com/2022/07/class-11-set-chapter-notesclass-11.html
