Class 11 Maths NCERT Solutions Chapter 1 Sets Exercise 1.1
EXERCISE
1.1
1. Which of the following
are sets ? Justify your answer.
(i)
The collection of all the months of a year
beginning with the letter J .
Answer:- To
determine if the given statement is a set. A set is a collection of well
defined objects we can definitely identify the collection of months beginning with a letter J.
Therefore, The
collection of all months of a year beginning with the letter J is the a set .
{June, July}
(ii)
The collection of ten most talented writers
of India.
Answer:- The collection of ten
most talented
writers of India is not a well defined collection as the criteria to determine
a writer’s talent many differ from one person to another.
Therefore, This collection is not a set .
(iii)
A team of eleven best – cricket batsman of
the world.
Answer:- A team of eleven best – cricket batsman of the world is
not a well defined collection. Because the criteria for determining a batsman’s
talent may very person to person.
Therefore, This collection is not a set .
(iv)
The collection of all boys your class.
Answer:- The collection of all boys
your class is well defined 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.
Answer:- The collection of all natural numbers less than 100 is
well defined collection. Because one can definitely identify a number that
belongs to this collection.
Therefore, This collection is a
set .
(vi)
A collection of novels written by the
writer Munshi Prem Chand.
Answer:- A collection of novels written by the writer Munshi
Prem Chand is well defined collection as one can find a book which belongs to
this collection.
Therefore, This collection is a
set .
(vii)
The collection of all even integers.
Answer:- The collection of all even integers is well
defined collection. Because one can definitely indentify an even integer that
belongs to this collection.
Therefore, This collection is set .
(viii)
The collection of question in this Chapter.
Answer:- The
collection of question in this Chapter is well defined collection. Because any
one can easily identify a questions that belongs to this Chapter.
Therefore, This collection is a set
.
(ix)
A
collection of most dangerous animals of the world.
Answer:- A collection of most dangerous animals of the world is
not a well defined collection. Because the criteria for determining the
dangerous of an animal can very from person to person.
Therefore, This collection is
not a set .
Class 11 Maths Chapter 1 Exercise
1.1 question 2
2. Let A = {1, 2, 3, 4,
5, 6} . Insert the appropriate symbol ϵ 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 ϵ A
(ii) 8 ∉
A
(iii) 0 ∉ A
(iv) 4 ϵ A
(v) 2 ϵ
A
(vi) 10 ∉ A
Class 11 Maths Chapter 1 Exercise 1.1 question 3
3. Write the following
sets in the 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 }
The required numbers are -3, -2, -1, 0, 1, 2, 3, 4, 5 and 6 only .
Therefore the given set in the
roster form is
A = { -3, -2, -1, 0, 1, 2, 3,
4, 5, 6 }
(ii)
B = { x : x is a natural number less than 6 }
The required numbers are 1, 2, 3, 4 and 5 only.
Therefore the given set in
the roster form is
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 }
The required numbers are 17, 26, 35, 44, 53, 62, 71 and 80 only.
Therefore the given set in
the roster form is
C = { 17, 26, 35, 44, 53, 62,
71, 80 }
(iv)
D = { x : x is a prime number which is divisor of 60}
60 = 2 × 2 × 3 × 5
The required numbers are 2, 3 and 5 only.
Therefore the given set in
the roster form is
C = { 2, 3, 5 }
(v)
E = The set of all letters in
the word TRIGONOMETRY
There are twelve letters in the TRIGONOMETRY, out of which letters T, R
and O are repeated.
Therefore, the given set in
the roster form is
E = { T, R, I, G, O, N, M, E,
Y }
(vi)
F = The
set of all letters in the word BETTER
There are six letters in the word BETTER, out of which letters E and T
are repeated.
Therefore, the given set in the roster form is
F = { B, E, T, R }
4. 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 }
We may write the set is
{ x : x = 3n, n ϵ N and 1 ≤ n ≤ 4 }
(ii)
{ 2, 4, 8, 16, 32 }
It can be seen that 2 = 21, 4= 22,
8 = 23, 16 = 24, 32 = 25
We may write the set is
{ x : x =2n ,
n ϵ
N and 1 ≤ n ≤ 5 }
(iii)
{ 5, 25, 125, 625 }
It can be seen that 5 = 51,
25 = 52 , 125 = 53, 625 = 54
We may write the set is
{ x : x =5n ,
n ϵ
N and 1 ≤ n ≤ 4 }
(iv)
{ 2, 4, 6, . . . }
It is a set of all even
natural numbers
Therefore, we may write this set is
{ 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
Therefore we may write this set is
{ x : x = n2, n ϵ N and 1 ≤ n ≤
10 }
Class 11 Maths Chapter 1 Exercise 1.1 question 5
5. List all the elements of the following sets :
Solution:
(i)
A = { x : x is an odd natural number }
The required numbers are
1, 3, 5, 7, 9, 11, 13, ……….
Therefore
A = { 1, 3, 5, 7, 9, 11, 13, ………. }
It can seen that (-1)2
= 1 ≤ 4 ; (-2)2 = 4 ≤ 4 ; 02 = 0 ≤ 4; 12 = 1 ≤
4 ; 22 = 4 ≤ 4
Therefore C = { -2, -1, 0, 1, 2 }
(iv)
D = { x : x is a letter in the word “LOYAL” }
There are five letters in the word LOYAL, out
of L is repeated.
Therefore
D = { L, O, Y, A }
(v)
E = { x : x is a months 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
precedes k } .
So, the elements are F = {
b, c, d, f, g, h, j }
Class 11 Maths Chapter 1 Exercise 1.1 question 6
6. Match each of the set
on the left in the roster form with the same set on the right described in set-builder
form :
(i)
{ 1, 2, 3, 6 } (a) x : x is a prime number and 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)
All the elements of this set are natural
numbers well as the divisors of 6.
Therefore, (i) matches with (c)
(ii)
It can be seen that 2 and 3 are prime
numbers. They are also the divisors of 6.
Therefore, (ii) matches with (a)
(iii)
All
the elements of this set are letters of the word MATHEMATICS .
Therefore, (iii) matches with (D)
(iv)
All the elements of this set are odd
natural numbers less than 10.
Therefore, (iv) matches with (b)
Published by : lokesh das
