Sets RS Aggarwal ICSE Class-6th Mathematics Solutions Goyal Brothers Prakashan Chapter-7. We provide step by step Solutions of Exercise / lesson-7 Sets for ICSE Class-6 RS Aggarwal Mathematics.
Our Solutions contain all type Questions with Exe-7 A , Exe-7 B, to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics.
| Board | ICSE |
| Publications | Goyal brothers Prakshan |
| Subject | Maths |
| Class | 6th |
| Chapter-7 | Sets |
| Writer | RS Aggrawal |
| Book Name | Foundation |
| Topics | Solution of Exe-7 A , Exe-7 B |
| Academic Session | 2021-2022 |
Sets RS Aggarwal ICSE Class-6th Maths Goyal Brothers Prakashan
–: Select Topics :–
Set Definition- A collection of well define Items / Group / Class / Category
Set Theory Rules
In mathematics, we follow some rules for the representation of sets. The rules are:
- The name of the set is denoted by upper case alphabet letters.
- The elements or members or objects of the set are denoted by lower case alphabet letters.
- If ′a′ belongs to A, this is represented as a∈A. Here,∈ is a Greek symbol, called epsilon. ∈ denotes “belongs to”. If ′c′ doesn’t belong to set A, we write it as c∉A.
Set Representation
Sets can be represented in two ways:
Roster Form
Roster or Tabular Form: In this form, all the elements of the set are listed, separated by commas and enclosed between curly braces { }
If A represents a set which contains all the letters in the word APPLE S, the proper Roster form representation would be
Ex- A ={A,P,L,E,S }
Set Builder Form
Set-builder Form: In this form, all the elements have a common property. This property is not applicable for the objects that do not belong to the set
. E.g. If set B has all the elements which are prime numbers, it is represented as:
S={ x: x is an prime number}
Types of Sets
The different types of sets in set theory are:
- Finite set
- Infinite set
- Empty set
- Singleton set
- Equal set
- Equivalent set
- Power set
- Universal set
- Subse
Exercise – 7 A, Sets RS Aggarwal ICSE Class-6th Mathematics Solutions Goyal Brothers Prakashan
Page 129
Question 1:
which are the following collections are set ? if any collections is not set , give reason
(i) All persons on earth
(ii) All male teachers of your school
(iii)All leaders of India
(iv) All healthy people of your town
(v) All fat boys of your locality
(vi) All planets in our solar system
(vii) All difficult problems in your book on Mathematics
(viii) All 3-digit natural numbers
(ix) All books in your school library
Answer :
(i) It is a set.
(ii) It is a set.
(iii) Not a set as there is no definition of being a “leader’
(iv) It is not a set as healthy is not well defined.
(v) It is not a set “fat” is not well-defined.
(vi) It is a set.
(vii) It is not a set “difficult” is not well-defined.
(viii) It is a set.
(ix) It is a set.
Question 2:
Describe each of the following sets in Roster form :
(i) A = {x : x is a natural number, 5 < x < 14}
(ii) B = {x : x is a factor of 18}
(in) C = {x : x is a prime factor of 330}
(iv) D = {x : x is a 2-digit number, the sum of whose digits is 8}
(v) E = {x : x is a natural number, x is a multiple of 7, x <60 }
(vi) F = {x : x is a natural number, x is neither prime nor composite}
(vii) G = {x : x is an even prime number}
(viii) H = {x : x is an odd natural number, 50 < x < 60}
Answer :
(i) A = {x : x is a natural number, 5< x < 14}
= {6, 7, 8, 9, 10, 11, 12, 13}
(ii) B = {x : x is a factor of 18}
= {1, 2, 3, 6, 9, 18}
(iii) C = {x : x is a prime factor of 330}
= {2, 3, 5, 11}
(iv) D = {x : x is a 2-digit number, the sum of whose digits is 8}
= {17,26, 35, 44, 53, 62, 71, 80}
(v) E = {x : x is a natural number, x is a multiple of 7, x < 60}
= {7, 14, 21, 28, 35, 42, 49, 56}
(vi) F = {x : x is a natural number, x is neither prime nor composite}
= {1}
(vii) G= {x : x is an even prime number}
= {2}
(viii) H = {x : x is an odd natural number, 50 <x < 60}
= {51, 53, 55, 57, 59}
Question 3:
Describe each of the following sets in set-builder form :
(i) A = {16, 18, 20, 22, 24, 26, 28}
(ii) B (23, 25, 27, 29, 31, 33, 35}
(iii) C = {1, 3, 5, 9, 15, 45}
(iv) D = {15, 24, 33, 42, 51, 60}
(v) E = {6, 12, 18, 24, 30, 36, 42, 48}
(vi) F = {41, 43, 47, 53, 59, 61, 67, 71, 73}
(vii) G = {0, 1, 4, 9, 16, 25, 36, 49}
Answer :
(i) A = {16, 18, 20, 22, 24, 26, 28}
= {x : x is an even natural number, 15 < x< 30}
(ii) B = {23, 25, 27, 29, 31, 33, 35}
{x : x is an odd natural number, 22 < x < 36)
(iii) C = {1,3,5,9, 15, 45}
= {x : x is a factor of 45}
(iv) D = {15, 24, 33, 42, 51, 60}
= {x : x is a 2-digit number and sum of digit is 6}
(v) E = {6, 12, 18, 24, 30, 36, 42, 48}
= {x : x is a multiple of 6, x < 50}
(vi) F = {41, 43, 47, 53, 59, 61, 67, 71, 73}
= {x : x is a prime between 40 and 75}
(vii) G = {0, 1, 4, 9, 16, 25, 36, 49}
= {x : x = n², n is a whole number 0 ≤ n ≤ 7}
Question 4:
Let A = {5, 7, 11, 13, 17, 19, 23, 29}.
Insert the appropriate symbol ∈ or ∉ in the blank spaces,
(i) 7 …………. A
(ii) 9 ……….. A
(iii) 3 ………………. A
(iv) 15 ……. A
(v) 17 ……. A
(vi) 25 … …… A
(vii) 11 ………….. A
(viii) 31 ……………. A
Answer :
(i) 7 ∈ A
(ii) 9 ∉ A
(iii) 3 ∉ A
(iv) 15 ∉ A
(v) 17 ∈ A
(vi) 25 ∈ A
(vii) 11 ∈ A
(viii) 31 ∈ A
Question 5:
Let B ={2,4, 6, 8, 10……………… 74, 76, 78, 80}.
Insert the appropriate symbol ∈ or ∉ in the blank spaces,
(i) 26 ………….. B
(ii) 31 ………….. B
(iii) 70 ………….. B
(iv) 15 ………….. B
(v) 60 ………….. B
(vi) 53 ………….. B
(vii) 47 ………….. B
(viii) 34 ………….. B
Answer :
(i) 26 ∈ B
(ii) 31 ∉ B
(iii) 70 ∈ B
(iv) 15 ∉ B
(v) 60 ∈ B
(vi) 53 ∉ B
(vii) 47 ∉ B
(viii) 34 ∈ B
Question 6:
State whether the given statement is true or false :
(i) 0 ∈ {x : x is a whole number, x < 10}
(ii) -5 ∈ {x : x is an integer, 4 <x<4}
(iii) -2∈ {x : x is an integer, x = 4}
(iv) 2∈ {x : x is a prime number, 3 < x < 6}
(v) 83∈ {x: x is a prime number, x < 100}
Answer :
(i) True
(ii) False as -5 ∉ to the set.
(iii) True
(iv) False, 2<3 and 2 ∉ the set.
(v) True
RS Aggarwal ICSE Class-6th Mathematics Sets Exercise – 7 B Solutions Goyal Brothers Prakashan
Page 132-133
Question 1:
write each of the following set in roster form and write its cardinal number:
(i) A = {x : x ∈ W, X <6}
(ii) B = {x : x ∈ N is a multiple of 4, x < 30}
(iii) C = {x : x ∈ N, x is a prefect square, x < 30}
(vi) D= {x: x ∈ N, x is a composite number, 10 < x < 18}
(v) E = {x : x is an odd prime number, x < }18
(vi) F = {x : x ∈ N, 5 <x <6}
(vii) G = {x : x is a letter in the word ‘ALLAHABAD’}.
Answer :
(i) A {x : x ∈ W, x < 6}
= {0, 1, 2, 3, 4, 5}
n(A) = 6
(ii) B = {x : x ∈ N is a multiple of 4, x < 30}
= {4, 8, 12, 16, 20, 24, 28},
n(B) = 7
(iii) C = {x : x ∈ N, c is a perfect square, x < 30}
={1,4,9, 16, 25),
n(C)=5
(iv) D= {x : x ∈ N, x is a composite number, 10 <x< 18}
={12, 14, 15, 16},
n(D)= 4
(v) E = {x : x is an odd prime number, x <18}
= {3,5,7, 11, 13, 17},
n(E) = 6
(vi) F = {x : x ∈ N, 5 <x<6}
= {}
n(F) = 0
(vii) G = {x : x is a letter in the word ‘ALLAHABAD’}.
= {A, L, 1H, B, D},
n(G) = 5
Question 2:
Let : A = {x : x is a letter in the word INCREASE’}.
B = {x : x is a vowel in the word INCREASE’} and
C = {x : x is a consonant in the word ‘INCREASE”}
(i) Write A, B and C is Roster form.
(ii) Find n(A), n(B) and n(C).
Answer :
(i) A = {x : x is a letter in the word ‘INCREASE’}.
= {I,N,C,R,E,A,S}
B = {x : x is a vowel in the word ‘INCREASE’}
= {I, E, A}
C = {x : x is a consonant in the word ‘INCREASE’}
= {N, C, R, S}
(ii) n(A) = 7,
n(B) = 3,
n(C) = 4
Question 3:
Which of the following sets are equal?
(i) A = {x : x ∈ N, 1 <x < 3} and
B {x : x is prime, x is even}.
(ii) C = {x : x ∈ W, x<8} and
D = {x : x ∈ N, x<9}.
(iii) E = {x : x ∈ N, x is odd, x <6} and
F = {x : x ∈ N, x is a factor of 15, x < 15).
(iv) G= {x : x is a prime factor of 12} and
H= {x : x is prime, X<4}.
(v) Φ and {0}.
Answer :
(i) A = {x : x ∈ N, 1 <x < 3}
= {2}
B = { x : x is prime, x is even}
= {12}
So, A = B
They are equal sets.
(ii) C = {x : x ∈ W, x <8}
= {0, 1,2, 3, 4, 5, 6, 7}
D = { x : x ∈ N, x<9}
= {1,2,3, 4, 5, 6, 7, 8}
0 ∉ D and 8 ∉ C
So, C ∉ D
They are not equal but are equivalent.
(iii) E = {x : x ∈ N, x is odd, x <6}
= {1, 3, 5}
F = { x : x ∈ N, x is a factor of 15, x <15}
= {1,3, 5
E = F
They are equal sets.
(iv) G= {x : x is a prime factor of 12}
= {2, 3}
H = {x : x is prime, x<4}
= {2,3}
G = H.
They are equal sets.
(v) Φ and {0}.
They are not equal.
Question 4:
Which of the following are empty sets?
(i) A = {x : x ∈ N, x + 3 = 3)
(ii) B = {x : x ∈ W, x +5 = 5}
(iii) C = {x : x ∈ N, x is even, x is divisible by 3}
(iv) D = {x : x is a prime number, x<2}
(v) E = {x : x ∈ N, x <1}
(vi) F = { x : x ∈ N, 2x = 1}
(vii) G = {0}
Answer :
(i) A = {x : x ∈ N, x +3= 3)
x + 3 =3
x = 3 – 3 = 0
but it ∉ N
= {} or Φ
So, Set A is an empty set.
(ii) B = {x : x ∈ W, x +5 = 5}
x + 5 = 5
x = 5 – 5 = 0 ∈ W
So, B is not empty set.
(iii) C = {x : x ∈ N, x is even, x is divisible by 3}
= {6, 12, 18, ………..}
So, C is not empty set.
(iv) D = {x : x is a prime number, x<2}
={}
If, There is no prime number < 2
So, D is a an empty ex. Φ
(v) E = {x : x ∈ N, x <1}
= {} or Φ
If, There is no natural number less than 1
(vi) F = { x : x ∈ N, 2x = 1}
= Φ,
If, There is no natural number which is in friction
(vii) G = {0}
It is an empty set as G Has one element ex. 0.
Question 5:
Classify the following into finite and infinite sets :
(i) A= {x : x ∈ N, x < 100}
(ii) B= {x : x ∈ I, x < 100}
(iii) C= {x : x ∈ N, x > 100}
(iv) D= {x : x ∈ I, x > -1}
(v) E= {x : x ∈ N, x is multiple of 3}
(vi) F= {x : x ∈ N, x is a factor of 1000}
(vii) G= {x : x is a point on an arc of a circle }
(viii) H= {x : x is a diameter of a circle}
Answer :
(i) A= {x : x ∈ N, x < 100}
= {1, 2, 3,4, 5, 6, ……………… 99}
It is finite set as it has element from 1 to 99
(ii) B= {x : x ∈ I, x < 100}
It is infinite set as it has element < 100
ex. {……….. , -2, -1, 0, 1, 2, ……………99}
(iii) C= {x : x ∈ N, x > 100}
It is infinite set as it has infinite number of element which are greater than 100
ex. {101, 102, 103, 104, ………..}
(iv) D= {x : x ∈ I, x > -1}
It is infinite set, as it has infinite number of element which are greater than-1
ie. {0, 1, 2, 3, 4,
(v) E= {x : x ∈ N, x is multiple of 3}
= {3,6,9, 12, 15, ….}
It is an infinite set.
(vi) F= {x : x ∈ N, x is a factor of 1000}
It is a finite set as it has limited elements
{1,2,4, 5, 8, 10, …500, 1000}
(vi) G= {x is a point on an arc of a circle }
It is an infinite set as there are infinite number of points on an arc or a line.
(vii) H= {x is a diameter of a circle}
It is an infinite set as infinite number of diameters can be drawn to a circle.
Question 6:
Find whether the given statement is true of false:
(i) If P and Q are two sets such that n(P) = n(Q), then P = Q.
(ii) Two equivalent sets are always equal.
(iii) Two equal sets are always equivalent.
(iv) Let A {x : x is a letter in the word ‘ENGINEER’} Then, n(A)= 5.
(v) Let B= {x : x is consonants in the word ‘MANAGEMENT’) Then, n(B) = 4
(vi) Let C {x : x ∈ N, x is neither prime nor composite). Then, n(C)=1.
(vii) n Φ = 0.
(viii) {x : x ∈ I, x is neither positive nor negative} = Φ
Answer :
(i) If P and Q are two sets such that n(P) = n(Q), then P = Q False.
They are not always equal, but are always equivalent.
(ii) False, two equivalent sets are not always equal
(iii) True
(iv) True, A = {x : x is a letter in the word ENGINEER}
= {E, N, G, I, R}, n(A) = 5
(v) True as B = {x : x is a consonant in the word MANAGEMENT}
={M, N, G, L, T}, n(B) = 4
(vi) True = {x : x ∈ N, x is neither prime nor composite}
= {1}, n(C) = 1
(vii) True n(Φ) = 0 as Φ has no element or zero element.
(viii) False. {x : x ∈ I, x is neither positive nor negative) = 0
{0} as it has one element while Φ has no element.
Question 7:
Let A = {2, 4, 6, 8, 10} and B {x : x ∈ W, x < 5}.
(i) Find n(A) and n(B).
(ii) Are A and B equivalent sets ?
Answer :
A = {2, 4, 6, 8, 10},
B {0, 1,2, 3,4}
(i) n(A)=5,
n(B) =5
(ii) A and B are equivalent set
–: End of Sets RS Aggarwal ICSE Class-6th ICSE Class-6th Solutions :–
Return to- RS Aggarwal Solutions for ICSE Class-6 Goyal Brothers Prakashan
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