NCERT Solutions for Class 11 Maths Chapter 1 Set

Ans : (i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identify a month that belongs to this collection. Hence, this collection is a set. 
(ii) The collection of ten most talented writers of India is not a well-defined collection because the criteria for determining a writer's talent may vary from person to person. Hence, this collection is not a set, 
(iii) A tearn of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsrnan's talent may varv from person to person. Hence, this collection is not a set. 
(iv) The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection. Hence, this collection is a set, 
(v) The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection. Hence, this collection is a set. 
(vi) A collection of novels written by the writer Munshi Prenn Chand is a well-defined collection because one can definitely identify a book that belongs to this collection.
Hence, this collection is a set. 
(vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection. Hence, this collection is a Set. 
(viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter. Hence, this collection is a set. 
(ix) The collection of most dangerous mimals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person. Hence, this collection is not a set. 

Ans : \(\begin{array}{l}{\text { (i) } 5 \in \mathrm{A}} \\ {\text { (ii) } 8 \notin \mathrm{A}} \\ {\text { (iii) } 0 \notin \mathrm{A}}\end{array}\)
\(\begin{array}{l}{\text { (iv) } 4 \in \mathrm{A}} \\ {\text { (v) } 2 \in \mathrm{A}} \\ {\text { (vi) } 10 \notin \mathrm{A}}\end{array}\) 

Ans : \(\begin{array}{l}{\text { (i) } A=\{x : x \text { is an integer and }-3< x < 7\}} \\ {\text { The elements of this set are }-2,-1,0,1,2,3,4,5, \text { and } 6 \text { only. }} \\ {\text { Therefore, the given set can be written in roster form as }} \\ {A=\{-2,-1,0,1,2,3,4,5,6\}} \\ {\text { (ii) } B=\{x : x \text { is a natural number less than } 6\}} \\ {\text { The elements of this set can be written in roster form as }} \\ {\text { B }=\{1,2,3,4,5\}}\end{array}\)
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only.
Therefore, this 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 a divisor of 60}
  
∴60 = 2 × 2 × 3 × 5
The elements of this set are 2, 3, and 5 only.
Therefore, this set can be written in roster form as D = {2, 3, 5}.
(v) E = The set of all letters in the word TRIGONOMETRY
There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.
Therefore, this set can be written in roster form as
E = {T, R, I, G, O, N, M, E, Y}
(vi) F = The set of all letters in the word BETTER 
There are 6 letters in the word BETTER, out of which letters E and T are repeated.
Therefore, this set can be written in roster form as  
F = {B, E, T, R} 

Ans : (i) {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32}
It can be seen that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.
∴ {2, 4, 8, 16, 32} = {x: x = 2n, n∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625}
It can be seen that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.
∴ {5, 25, 125, 625} = {x: x = 5n, n∈N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6 …}
It is a set of all even natural numbers.
∴ {2, 4, 6 …} = {x: x is an even natural number}
(v) {1, 4, 9 … 100}
It can be seen that 1 = 12, 4 = 22, 9 = 32 …100 = 102.
∴ {1, 4, 9… 100} = {x: x = n2, n∈N and 1 ≤ n ≤ 10} 

Ans : (i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}
  


(iii) C = {x: x is an integer;}
It can be seen that
(–1)2 = 1 ≤ 4; (–2)2 = 4 ≤ 4; (–3)2 = 9 > 4
02 = 0 ≤ 4
12 = 1 ≤ 4
22 = 4 ≤ 4
32 = 9 > 4
∴C = {–2, –1, 0, 1, 2}


(iv) D = (x: x is a letter in the word “LOYAL”) = {L, O, Y, A}
(v) E = {x: x is a month of a year not having 31 days}
= {February, April, June, September, November}
(vi) F = {x: x is a consonant in the English alphabet which precedes k}
= {b, c, d, f, g, h, j}