11th SETS
 On 25/01/2013
 In MATHS
SETS
Exercise 1.1
Page 4
Q1: Which of the following are sets? Justify our answer.
(i) The collection of all months of a year beginning with the letter J.
Ans: (i) The collection of all months of a year beginning with the letter J is a welldefined 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.
ANS: (ii) The collection of ten most talented writers of India is not a welldefined 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 team of eleven bestcricket batsmen of the world.
ANS: (iii) A team of eleven best cricket batsmen of the world is not a welldefined collection because the criteria for determining a batsman’s talent may vary from person to person.
Hence, this collection is not a set.
(iv) The collection of all boys in your class.
ANS: (iv) The collection of all boys in your class is a welldefined 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.
ANS: (v) The collection of all natural numbers less than 100 is a welldefined 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 Prem Chand.
ANS: (vi) A collection of novels written by the writer Munshi Prem Chand is a welldefined 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.
ANS: (vii) The collection of all even integers is a welldefined 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.
ANS: (viii) The collection of questions in this chapter is a welldefined collection because one can definitely identify a question that belongs to this chapter.
Hence, this collection is a set.
(ix) A collection of most dangerous animals of the world.
ANS: (ix) The collection of most dangerous animals of the world is not a welldefined collection because the criteria for determining the dangerousness of an animal can vary from person to person.
Hence, this collection is not a set.
Page 5
Q2:Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:
(i) 5…A
Ans: (i) 5 ∈ A
(ii) 8…A
Ans: (ii) 8 ∉ A
(iii) 0…A
Ans: (iii) 0 ∉ A
(iv) 4…A
Ans: (iv) 4 ∈ A
(v) 2…A
Ans:(v) 2 ∈ A
(vi) 10…A
Ans:(vi) 10 ∉ A
Q3:Write the following sets in roster form:
(i) A = {x: x is an integer and –3 < x < 7}.
Ans:(i) A = {x: x is an integer and –3 < x < 7}
The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.
Therefore, 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}.
Ans: (ii) B = {x: x is a natural number less than 6}
The elements of this set are 1, 2, 3, 4, and 5 only.
Therefore, the given set can be written in roster form as
B = {1, 2, 3, 4, 5}
(iii) C = {x: x is a twodigit natural number such that the sum of its digits is 8}
Ans: (iii) C = {x: x is a twodigit 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 divisor of 60}.
Ans: (iv) D = {x: x is a prime number which is a divisor of 60}

2
60
2
30
3
15
5
∴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.
Ans: (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.
Ans: (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}
Q4:Write the following sets in the setbuilder form:
(i) (3, 6, 9, 12)
Ans: (i) {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32}
Ans: (ii) {2, 4, 8, 16, 32}
It can be seen that 2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}.
∴ {2, 4, 8, 16, 32} = {x: x = 2^{n}, n∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625}
Ans: (iii) {5, 25, 125, 625}
It can be seen that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.
∴ {5, 25, 125, 625} = {x: x = 5^{n}, n∈N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6 …}
Ans: (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}
Ans: (v) {1, 4, 9 … 100}
It can be seen that 1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}.
∴ {1, 4, 9… 100} = {x: x = n^{2}, n∈N and 1 ≤ n ≤ 10}
Q5: List all the elements of the following sets:
(i) A = {x: x is an odd natural number}
Ans: (i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}
(ii) B = {x: x is an integer,}
Ans: (ii) B = {x: x is an integer;}
It can be seen that and
∴ B
(iii) C = {x: x is an integer,}
Ans; (iii) C = {x: x is an integer;}
It can be seen that
(–1)^{2} = 1 ≤ 4; (–2)^{2} = 4 ≤ 4; (–3)^{2} = 9 > 4
0^{2} = 0 ≤ 4
1^{2} = 1 ≤ 4
2^{2} = 4 ≤ 4
3^{2} = 9 > 4
∴C = {–2, –1, 0, 1, 2}
(iv) D = {x: x is a letter in the word “LOYAL”}
Ans: (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}
Ans: (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 proceeds k}.
Ans: (vi) F = {x: x is a consonant in the English alphabet which precedes k}
= {b, c, d, f, g, h, j}