Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets

Selina Publishers Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets

Sets Exercise 6A – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Write the following sets in roster (Tabular) form :
(i) A1 = {x : 2x + 3 = 11}
(ii) A2 = {x : x2 – 4x – 5 = 0}
(iii) A3 = {x : x ∈ Z, -3 ≤ x < 4}
(iv) A4 = {x : x is a two digit number and sum of digits of x is 7}
(v) A5 = {x : x = 4n, n ∈ W and n < 4}
(vi) A6 = {x : x = \(\frac{n}{n+2}\); n ∈ N and n > 5}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 1
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 2
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 3

Question 2.
Write the following sets in set-builder (Rule Method) form :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 12
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 4

Question 3.
(i) Is {1, 2, 4, 16, 64} = {x : x is a factor of 32} ? Give reason.
(ii) Is {x : x is a factor of 27} ≠ {3, 9, 27, 54} ? Give reason.
(iii) Write the set of even factors of 124.
(iv) Write the set of odd factors of 72.
(v) Write the set of prime factors of 3234.
(vi) Is {x : x2 – 7x + 12 = 0} = {3, 4} ?
(vii) Is {x : x2 – 5x – 6 = 0} = {2, 3} ?
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 5
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 6

Question 4.
Write the following sets in Roster form :
(i) The set of letters in the word ‘MEERUT’.
(ii) The set of letters in the word ‘UNIVERSAL’.
(iii) A = {x : x = y + 3, y ∈N and y > 3}
(iv) B = {p : p ∈ W and p2 < 20}
(v) C = {x : x is composite number and 5 < x < 21}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 7
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 8

Question 5.
List the elements of the following sets :
(i) {x : x2 – 2x – 3 = 0}
(ii) {x : x = 2y + 5; y ∈ N and 2 ≤ y < 6}
(iii) {x : x is a factor of 24}
(iv) {x : x ∈ Z and x2 ≤ 4}
(v) {x : 3x – 2 ≤ 10, x ∈ N}
(vi) {x : 4 – 2x > -6, x ∈ Z}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 9
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 10
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6A 11

Sets Exercise 6B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find the cardinal number of the following sets :
(i) A1 = {-2, -1, 1, 3, 5}
(ii) A2 = {x : x ∈ N and 3 ≤ x < 7}
(iii) A3 = {p : p ∈ W and 2p – 3 < 8}
(iv) A4 = {b : b ∈ Z and -7 < 3b – 1 ≤ 2}
Cardinal Number of a set; The number of elements in a set is called is Cardinal Number.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 12
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 13

Question 2.
If P = {P : P is a letter in the word “PERMANENT”}. Find n (P).
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 14

Question 3.
State, which of the following sets are finite and which are infinite :
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 30
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 15
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 16
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 17

Question 4.
Find, which of the following sets are singleton sets :
(i) The set of points of intersection of two non-parallel st. lines in the same plane
(ii) A = {x : 7x – 3 = 11}
(iii) B = {y : 2y + 1 < 3 and y ∈ W}
Note : A set, which has only one element in it, is called a SINGLETON or unit set.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 18

Question 5.
Find, which of the following sets are empty :
(i) The set of points of intersection of two parallel lines.
(ii) A = {x : x ∈ N and 5 < x < 6}
(iii) B = {x : x2 + 4 = 0, x ∈ N}
(iv) C = {even numbers between 6 & 10}
(v) D = {prime numbers between 7 & 11}
Note : The set, which has no element in it, is called the empty or null set.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 19

Question 6.
(i) Are the sets A = {4, 5, 6} and B = {x : x2 – 5x – 6 = 0} disjoint ?
(ii) Are the sets A = {b, c, d, e} and B = {x : x is a letter in the word ‘MASTER’} joint ?
Note :
(i) Two sets are said to be joint sets, if they have atleast one element in common.
(ii) Two sets are said to be disjoint, if they have no element in common.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 20

Question 7.
State, whether the following pairs of sets are equivalent or not :
(i) A = {x : x ∈ N and 11 ≥ 2x – 1} and B = {y : y ∈ W and 3 ≤ y ≤ 9}
(ii) Set of integers and set of natural numbers.
(iii) Set of whole numbers and set of multiples of 3.
(iv) P = {5, 6, 7, 8} and M = {x : x ∈ W and x < 4}
Note : Two sets are said to be equivalent, if they contain the same number of elements.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 21
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 22

Question 8.
State, whether the following pairs of sets are equal or not :
(i) A = {2, 4, 6, 8} and
B = {2n : n ∈ N and n < 5}
(ii) M = {x : x ∈ W and x + 3 < 8} and
N = {y : y = 2n – 1, n ∈ N and n < 5}
(iii) E – {x : x2 + 8x – 9 = 0} and
F = {1, -9}
(iv) A = {x : x ∈ n, x < 3} and
B = {y : y2 – 3y + 2 = 0}
Note: Two sets are equal, if both the sets have same (identical) elements.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 23
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 24
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 25

Question 9.
State whether each of the following sets is a finite set or an infinite set:
(i) The set of multiples of 8.
(ii) The set of integers less than 10.
(iii) The set of whole numbers less than 12.
(iv) {x : x = 3n – 2, n ∈ W, n ≤ 8}
(v) {x : x = 3n – 2,n ∈ Z, n ≤ 8}
(vi) {x : x = \(\frac { n-2 }{ n+1 }\) , n ∈ w)
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 26

Question 10.
Answer, whether the following statements are true or false. Give reasons.
(i) The set of even natural numbers less than 21 and the set of odd natural numbers less than 21 are equivalent sets.
(ii) If E = {factors of 16} and F = {factors of 20}, then E = F.
(iii) The set A = {integers less than 20} is a finite set.
(iv) If A = {x : x is an even prime number}, then set A is empty.
(v) The set of odd prime numbers is the empty set.
(vi) The set of squares of integers and the set of whole numbers are equal sets.
(vii) In n(P) = n(M), then P → M.
(viii) If set P = set M, then n(P) = n(M).
(ix) n(A) = n(B) ⇒ A = B.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 27
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 28
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6B 29

Sets Exercise 6C – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Find all the subsets of each of the following sets :
(i) A = {5, 7}
(ii) B = {a, b, c}
(iii) C = {x : x ∈ W, x ≤ 2}
(iv) {p : p is a letter in the word ‘poor’}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 30

Question 2.
If C is the set of letters in the word “cooler”, find :
(i) Set C
(ii) n(C)
(iii) Number of its subsets
(iv) Number of its proper subsets.
Note : (i) If a set has n elements, the number of its subsets = 2n
(ii) If a set has n elements, the number of its proper subsets = 2n – 1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 31

Question 3.
If T = {x : x is a letter in the word ‘TEETH’}, find all its subsets.
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 32

Question 4.
Given the universal set = {-7,-3, -1, 0, 5, 6, 8, 9}, find :
(i) A = {x : x < 2}
(ii) B = {x : -4 < x < 6}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 33

Question 5.
Given the universal set = {x : x ∈ N and x < 20}, find :
(i) A = {x : x = 3p ; p ∈ N}
(ii) B = {y : y – 2n + 3, n ∈ N}
(iii) C = {x : x is divisible by 4}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 34

Question 6.
Find the proper subsets of {x : x2 – 9x – 10 = 0}
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 35

Question 7.
Given, A = {Triangles}, B = {Isosceles triangles}, C = {Equilateral triangles}. State whether the following are true or false. Give reasons.
(i) A ⊆ B
(ii) B ⊆ A
(iii) C ⊆  B
(iv) B ⊂ A
(v) C ⊂ A
(vi) C ⊆  B ⊆  A
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 36

Question 8.
Given, A = {Quadrilaterals}, B = {Rectangles}, C = {Squares}, D= {Rhombuses}. State, giving reasons, whether the following are true or false.
(i) B ⊂ C
(ii) D ⊂ B
(iii) C ⊆ B ⊆ A
(iv) D ⊂ A
(v) B ⊇ C
(vi) A ⊇ B ⊇ D
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 37

Question 9.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C Q9
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 38

Question 10.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C Q10
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 39

Question 11.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C Q11
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 40

Question 12.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C Q12
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6C 41

Sets Exercise 6D – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 42

Question 2.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 43

Question 3.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q3
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q3.1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 44

Question 4.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 45
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 46

Question 5.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 47
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 48

Question 6.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 49
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 50

Question 7.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 51

Question 8.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q8
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 52

Question 9.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D Q9
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 53
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6D 54

Sets Exercise 6E – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 55

Question 2.
From the given diagram, find :
(i) A’
(ii) B’
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q2
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 56

Question 3.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q3
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 57

Question 4.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q4
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 58

Question 5.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q5
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 59

Question 6.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q6
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 60

Question 7.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q7
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 61

Question 8.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q8
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q8.1
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 62

Question 9.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q9
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 63

Question 10.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q10
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 64

Question 11.
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E Q11
Solution:
Selina Concise Mathematics Class 8 ICSE Solutions Chapter 6 Sets Ex 6E 65

Selina Concise Mathematics Class 8 ICSE Solutions