Solutions of CBSE Class XI NCERT Mathematics
Chapter 1, sets
CBSE Class 11 NCERT Mathematics Solutions of Exercise 1.1
(Cbse Class 11 Ncert
Math Textbook Page 4)
Question 1: 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 bestcricket
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 welldefined collection of objects because we
can definitely identify a month that belongs to this collection. So, this
collection is a set.
(ii) The collection of ten most talented writers
of India is not a welldefined collection since the criteria for determining a
writer’s talent could vary from person to person. So, this collection is not a
set.
(iii) A team of eleven best cricket batsmen of the
world is not a welldefined collection as the criteria for determining a
batsman’s talent will vary from person to person. Hence, this collection cannot
be termed a set.
(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 is a welldefined collection because each number that belongs to this
collection is a definite number. Hence, this collection is a set.
(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 is a
welldefined collection because one can definitely identify an even integer
that belongs to this collection. So, this collection is a set.
(viii) The collection of questions in this chapter
is a welldefined collection because one can definitely identify a question
that belongs to this chapter and hence, this collection is a set.
(ix) The collection of most dangerous animals of
the world is not a set. Because the criteria for determining the dangerousness
of an animal can vary from person to person and the collection will also vary.
Question 2: 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
Question
3: 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
twodigit 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}
The elements
of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.
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}
The elements
of this set are 1, 2, 3, 4, and 5 only.
Hence, 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}
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
Hence, the
elements of this set are 2, 3, and 5.
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. Hence, 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}
CBSE Class 11 Mathematics NCERT Solutions of Chapter 1, Sets Exercise 1.1
Question 4: Write the following
sets in the setbuilder 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} = {x: x = 3n, n ∈ N and 1 ≤ n
≤ 4}
(ii) In the
given set, 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}
It can be
seen that 5 = 5^{1} , 25 = 5^{2} , 125 = 5^{3} , and
625 = 5^{4}
Therefore,
{5, 25, 125, 625} = {x: x = 5^{n}, n ∈
N
and 1 ≤ n ≤ 4}
(iv) {2,
4, 6 …} is a set of all even natural numbers.
∴ {2, 4, 6 …} = {x: x is an even natural
number}
(v) {1,
4, 9 … 100}
In the given
set of numbers, 1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 =
10^{2}.
∴ {1, 4, 9… 100} = {x: x = n2, n ∈ N and 1 ≤ n ≤ 10}
Question
5: List all the elements of the following sets:
Solution:
(i) A = {x:
x is an odd natural number} = {1, 3, 5, 7, 9 …}
(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}
Question 6: Match each of the set on the left in the roster form with
the same set on the right described in setbuilder form:
(i) {1, 2, 3, 6}

(a) {x: x is a prime number and a divisor of 6}

(ii) {2, 3}

(b) {x: x is an odd natural number less than 10}

(iii) {M, A,T, H, E, I,C, S}

(c) {x: x is natural number and divisor of 6}

(iv) {1, 3, 5, 7, 9}

(d) {x: x is a letter of the word MATHEMATICS}

Solution:
(i) – (c); Because all
the elements of this set are natural numbers as well as the divisors of 6.
(ii) – (a); It can
be seen that 2 and 3 are prime numbers and are also the divisors of 6.
(iii) – (d); Since all the elements of this
set are letters of the word MATHEMATICS.
(iv) – (b); as all
the elements of this set are odd natural numbers less than 10.