Class 8: Chapter 1 – Sets – Exercise 1B
1. Write down the following statements, using set notation:
i. Set A is a proper subset of set B
Answer: A B
Note: Let A be any set and B a non-empty set. Then, A is called a proper
subset of B is all elements of A exists in the set B but B has at least one
element that is not in set A.
ii.
Set C is a superset of set D
Answer: C D
Note: If A is a subset of set B, then B is called the super set of A.
iii.
Set B contains set A
Answer: B A
Note: If B contains set A, that means that B is a super set of A.
iv.
Neither A is a subset of B, nor B is a subset of A
Answer: A B and B  A
Note: If there exists even a single element in set A that does not exist in the set
B, then A is not a subset of B. Similarly, if there is any element in B that does
not exist in set A, then B is not a subset of A.
2. Let A = {all quadrilaterals}, B = {all rectangles}, C = {all squares} and D = {all
rhombuses} in a plane. State, giving reasons, whether the following statements are true or
false.
i. B  C  A
Answer: False
Note: All rectangles are not squares and hence B is not a proper subset of C.
All squares are quadrilaterals and hence C is a proper subset of A.
ii.
CBA
Answer: True
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Note: All squares are also rectangles, and all rectangles are quadrilaterals.
iii.
CDA
Answer: True
Note: All squares are rhombuses and all rhombuses are quadrilaterals.
iv.
DCA
Answer: False
Note: All rhombuses are not squares.
v.
ABC
Answer: True
Note: A is a super set of B and B is a super set of C. This is because, all
quadrilaterals will contain all rectangles and all rectangles would contain all
squares.
vi.
AB C
Answer: False
Note: All rectangles need not contain all quadrilaterals. And all squares need
not contain all rectangles.
3. Let A = {all triangles}, B = {all isosceles triangles} and C = {all equilateral triangles}.
State, giving reasons, whether the following statements are true or false
i. B  C A
Answer: False
Note: All isosceles triangles are not equilateral triangles.
ii.
C BA
Answer: True
Note: All equilateral triangles are isosceles triangles and all isosceles
triangles are triangles
4. Let A = {1, 2}. State which of the following statements are true:
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i.
1A
Answer: False
Note: 1 is an element of set A. 1 is not a set.
ii.
{1} A
Answer: False
Note: {1} is a set. It does not belong to A. The element 1 belongs to A.
iii.
1 A
Answer: True
Note: 1 is an element of set A.
iv.
 A
Answer: False
Note: does not belong to set A. means a null or empty set.
v.
A
Answer: True
Note: Null set is a subset of set A.
vi.
{1} A
Answer: False
Note: {1} is a subset. Element belong or not belong to set A.
5. Which of the following statements are correct?
i. a  {a, b, c}
Answer: False
Note: a is an element of the set {a, b, c}. Hence it should be a  {a, b, c}
ii.
{a}  {a, b, c}
Answer: False
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Note: {a} is subset of the set {a, b, c}. Hence it should be a  {a, b, c}
iii.
{a}  {a, b, c}
Answer: Correct
Note: {a} is subset of the set {a, b, c}. Hence it should be a  {a, b, c}
iv.
 {a, b, c}
Answer: False
Note: is not an element of {a, b, c}. It should be  {a, b, c}
v.
  {a, b, c}
Answer: Correct
vi.
{ }  {a, b, c}
Answer: False
Note: {a, b, c} does not contain {}
vii.
a  {{a}, b}
Answer: False
Note: a does not belong to {{a}, b}, but {a} belongs to {{a}, b}
viii.
{a}  {{a}, b}
Answer: False
Note: {a} is an element of the set {{a}, b} and not a set.
ix.
{a, b}  {{a, b}, c}
Answer: Correct
Note: {a, b} belong to {{a, b}, c} as {a, b} is an element of the set {{a, b}, c}
6. Which of the following statements are true?
i. 
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Answer: False
Note: The set contains 0 as an element. It is not a null set.
ii.

Answer: False
Note: The set contain as the element. It is not a null set.
iii.

Answer: False
Note: does not belong to the set {0}
iv.

Answer: True
Note: is an element in the set 
v.

Answer: True
Note: is an element of the set 
vi.

Answer: False
Note: 
7. Which of the following statement are true?
i. For any two sets A and B, either A  B or B  A
Answer: False
Note: For A to be a subset of B, all elements of A should be in B. This need
not be true as A can have elements that are not in B and B can have elements
that are not in A. Hence it is not necessary that for any two sets A and B,
either A  B or B  A is always true.
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ii.
Every subset of a finite set is a finite set
Answer: True
Note: Finite set is a set where the counting process of the elements comes to
an end. Basically, the set contains finite elements that can be counted. So, if
the set has finite elements, then all the subsets will also be finite.
iii.
Every subset of an infinite set is infinite
Answer: False
Note: Let A= {1, 2, 3, 4, 5 …}. Then {1} is a subset of A. Though A is infinite,
the subset {1} is finite.
iv.
Every set has a proper subset
Answer: False
Note: No. The null set cannot have a proper subset. For any other set, the null
set will be a proper subset. There will also be other proper subsets.
v.
If A has n elements, then P(A) has 2n subsets
Answer: True
Note: The set of all possible subsets of a set A is called the power set of A, and
is denoted by P(A). If A contains n elements, then P(A) contains 2n subsets.
8. Let A be the set of letters in the word ‘seed’. Find
i. A
Answer: A = {s, e, d}
ii.
n(A)
Answer: 3
iii.
number of subset of A
Answer: 23=8
Note: The set of all possible subsets of a set A is called the power set of A, and
is denoted by P(A). If A contains n elements, then P(A) contains 2n subsets.
iv.
number of proper subsets of A
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Answer: (23 – 1) = 7
Note: A set containing n elements has (2n – 1) proper subsets.
9. Find all possible subsets of each of the following sets:
i. A = {4, 9}
Answer:  {4}, {9}, {4, 9}
Note: Number of elements = 2. Total subsets =22 = 4
ii.
B = {2, 3, 8}
Answer:  {2}, {3}, {8}, {2, 3}, {2, 8}, {3, 8}, {2, 3, 8}
Note: Number of elements = 3. Total subsets = 23 = 8
iii.
C = {0, 1, 2}
Answer:  {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}, {0, 1, 2}
Note: Number of elements = 3. Total subsets = 23 = 8
10.Find the power set of each of the following:
i. A = {0, 5}
Answer: P(A) = { , {0}, {5}, {0, 5}}
Note: P(A) = Set of all possible subsets of set A
ii.
B = {7, 9}
Answer: P(A) = { , {7}, {9}, {7, 9}}
iii.
C = {2, 4, 6}
Answer: P(A) = { , {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6}}
11.Let A = {1, {2}}. Find the power of set A.
Answer: P(A) = {{1}, {{2}}, {1, {2}} }
Note: consider {2} as an element.
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12.Let x : x  N, x < 50}, A = {x : x2  x : x = n2, n  N} and C = {x : x is a
factor of 36}. List all the elements of set A, B, and C. Also state whether each of the
following statement is true or false.
Answer:
Basically x is values from 1 to 49. Therefore:
A = {1, 2, 3, 4, 5, 6, 7}.
B = {1, 4, 9, 16, 25, 36, 49}
C = {1, 2, 3, 4, 6, 9, 12, 18, 36}. All factors of 36 but within 1 <= x <= 49
i.
AB
Answer: False
ii.
A=B
Answer: False
iii.
AB
Answer: True since n(A) = 7 while n(B) = 7.
iv.
BC
Answer: False since n(B) = 7 while n(C) = 9
v.
n(A) < n(C)
Answer: True since n(A) = 7 while n(C) = 9
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