Math Class VIII 1 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
Section I : Sets
1. Describe the following sets in roster form :
(i) 2{ / , , 2 5}x x n n N n= ∈ ≤ ≤
(ii) {x / x is composite number and 11 < x < 25}
(iii) {x / x ∈ W, x is divisible by 4 and 6, x ≤ 100}
(iv) {x / x is two digit number whose sum of digits is 7}
(v) / , and 5
3
n
x x n N n
n
= ∈ ≤
+
(vi)
2 1
/ , and 10
2 3
n
x x n W n
n
+
= ∈ ≤
+
(vii) 2{ / , 20}x x W x∈ <
(viii) 2{ / 5 , and 400}x x p P I x= ∈ <
(ix)
1
/ , and 5x x n N n
n
= ∈ ≤
(x) { /3 – 5 15, }x x x W< ∈
(xi) {First four planets of our solar system}.
Ans. (i) {4, 9, 16, 25}
(ii) {12, 14, 15, 16, 18, 20, 21, 22, 24}
(iii) {0, 12, 24, 36, 48, 60, 72, 84, 96}
(iv) {16, 25, 34, 43, 52, 61, 70}
(v)
1 2 3 4 5
, , , ,
4 5 6 7 8
12
SETS AND VENN
DIAGRAMS
Math Class VIII 2 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
(vi)
1 3 5 7 21
, , , ,
3 5 7 9 23
⋅ ⋅ ⋅
(vii) {– 4, – 3, – 2, – 1, 0, 1, 2, 3, 4}
(viii) {– 15, – 10, – 5, 0, 5, 10, 15}
(ix)
1 1 1 1
1, , , ,
2 3 4 5
(x) {0, 1, 2, 3, 4, 5, 6}
(xi) {Mercury, Venus, Earth, Mars}
2. Write the following sets in the builder form :
(i) {11, 13, 17, 19, 23, 29, 31, 37}
(ii)
1 1 1
1, , , ,
2 3 9
⋅ ⋅⋅
(iii) {21, 23, 25, 27, 29, 31, 33, 35, 37}
(iv)
1 3 5 7
, , , ,
3 5 7 9
⋅ ⋅ ⋅
(v) {– 10, – 5, 0, 5, 10, 15, …, 100}
(vi) {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.
Ans. (i) {x / x is a prime number, 10 < x < 40}.
(ii)
1
/ , and 10x x n N n
n
= ∈
Math Class VIII 3 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
3. Find, which of the following sets are singleton set :
(i) The set of points of intersection of two non-parallel straight
lines on the same plane.
(ii) A = {x : 7x – 3 = 11}
(iii) B = {y : 2y + 1 < 3 and y ∈ W}
Ans.(i) The set of points of intersection of two non-parallel straight
lines on the same plane is a singleton set.
(ii) A = {x : 7x – 3 = 11}
7x – 3 = 11 ⇒ 7x = 11 + 3
⇒ 7x = 14 ⇒ x =
14
2
7
=
∴ A = {2}
Hence, the given set A has only one element, so it is a singleton set.
(iii) B = {y : 2y + 1< 3 and y W∈ }
2y + 1 < 3
⇒ 2y + 1 – 1 < 3 – 1 (Subtracting 1 from both sides)
⇒ 2y < 2
⇒ y <
2
2
(Dividing both sides by 2)
⇒ y < 1
∴ B = {0}
Hence, it is a singleton set.
4. 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 whole numbers and set of multiples of 3.
(iii) P = {5, 6, 7, 8} and M = {x : x ∈ W and x ≤ 4}
Ans. (i) A = {x : x ∈ N and 11 ≥ 2x – 1}
11 ≥ 2x – 1
⇒ 11 + 1 ≥ 2x – 1 + 1 ( Adding 1 to both sides)
Math Class VIII 4 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
⇒ 12 ≥ 2x ⇒
12
2
≥ x ⇒ 6 ≥ x
∴ A = {1, 2, 3, 4, 5, 6}
∴ n(A) = 6
B = {y : y W∈ and 3≤ y ≤ 9}
∴ 3 ≤ y ≤ 9
∴ B = {3, 4, 5, 6, 7, 8, 9}
∴ n (B) = 7
∴ Cardinal number of set A = 6 and cardinal number of
set B = 7
Hence, set A and set B are not equivalent.
(ii) Set of whole numbers and set of multiples of 3 are equivalent
because both these sets have infinite number of elements.
(iii) P = {5, 6, 7, 8}
n (P) = 4
M = {x : x ∈ W and x ≤ 4}
M = {0, 1, 2, 3, 4}
n(M) = 5
Cardinal number of set P = 4
and Cardinal number of set M = 5. Hence, these sets are not
equivalent.
5. (A) Let A = {all quadrilaterals}, B = {all rectangles}, C = {all
squares} and D = {all rhombuses} in a plane. State, whether the
following statements are true or false.
(i) B C A⊂ ⊂ (ii) C B A⊂ ⊂
(iii) C D A⊂ ⊂ (iv) D C A⊂ ⊂
(v) A B C⊇ ⊇ (vi) A B C⊆ ⊆
Ans.(i) False (ii) True (iii) True (iv) False (v) True (vi) False
(B) Let A = {all triangles}, B = {all isosceles triangles} and C = {all
equilateral triangles}. State whether the following statements are
true or false.
Math Class VIII 5 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
(i) B C A⊂ ⊂ (ii) C B A⊂ ⊂
Ans. (i) False (ii) True
6. Let A be the set of letters in the word, ‘seed’. Find:
(i) A (ii) n (A)
(iii) Number of subsets of A (iv) Number of proper subsets
Ans. (i) A = {s, e, d}
(ii) n (A) = number of elements = 3
(iii) Number of subsets of A = 23 = 8
{ }, {s}, {e}, {d}, {s, e}, {s, d}, {e, d} {s, e, d}.
(iv) Number of proper subsets of A
= 2n – 1= 23 – 1 = 8 – 1= 7
because { } or φ is not a proper subset.
7. (A) Find the power set of each of the following sets :
(i) A = {0, 5} (ii) B = {7, 9} (iii) C = {2, 4, 6}
Ans. (i) P (A) = {φ , {0}, {5}, {0, 5}}.
(ii) P (B) = {φ , {7}, {9}, {7, 9}}.
(iii) P (C) = {φ , {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6}}.
(B) Let A = {1, {2}}. Find the power set of A.
Ans. (i) P (A) = {φ , {1}, {{2}}, {1, {2}}.
8. Let { : , 50},x x N xξ = ∈ < 2{ : },A x x= ∈ξ 2{ : ,B x x n= =
}n N∈ and C = {x : x is a factor of 36}. List the elements of each
of the sets A, B and C. Also, state whether each of the following
statements is true or false :
(i) A B⊆ (ii) A = B (iii) A B↔
(iv) B C↔ (v) n (A) < n (C)
Ans. ξ = { : , 50}x x N x∈ < = {1, 2, 3, 4, 5, …, 49, 50}
A =
2
{ : }x x ∈ξ = {1, 2, 3, 4, 5, 6, 7}
Math Class VIII 6 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
B = {x : x = n2, n ∈ N} = {1, 4, 9, 16, 25, 36, 49}
C = {x : x is a factor of 36}
= {1, 2, 3, 4, 6, 9, 12, 18, 36}
(i) False (ii) False (iii) True
(iv) False (v) True
9. Let A = {letters of BOMBAY} and B = {letters of CALCUTTA}
(i) Are these sets disjoint or overlapping ?
(ii) Are these sets equal ?
(iii) Are these sets equivalent ?
(iv) Is any of these sets, subset of the other ?
(v) Describe a universal set for this problem.
Ans. A = {letters of BOMBAY} = {A, B, M, O,Y}
B = {letters of CALCUTTA} = {A, C, L, T, U}.
(i) These sets are overlapping.
(ii) These sets are not equal.
(iii) These sets are equivalent.
(iv) Neither A B⊆ nor B A⊆ .
(v) {Letters of English alphabet}.
10. Let { : , 15},x x W xξ = ∈ < A = {multiples of 2}, B = {multiples of 3},
C = {multiples of 5} and D = {multiples of 6}
State whether each of the following statements is true or false :
(i) C and D are disjoint (ii) C D↔ (iii) C = D
(iv) A B↔ (v) A B⊇ (iv) D A⊆
(vii) D B⊆ (viii) C B⊆
Ans. The sets ,ξ A, B, C and D in roster form are
ξ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
A = {2, 4, 6, 8, 10, 12, 14}
B = {3, 6, 9, 12}
Math Class VIII 7 Question Bank
© E
D
U
LA
BZ
IN
TE
R
N
AT
IO
N
AL
C = {5, 10}
D = {6, 12}
(i) True (ii) True
(iii) False, because C and D are disjoint sets.
(iv) False, because A has more elements than B
(v) False, because B is not contained in A.
(vi) True (vii) True
(viii) False, because C is not contained in B.
11. Given the universal set = { : and 20},x x N x∈ < find :
A = {x : x = 3p ; p ∈ N}
Ans. Universal set U = {x : x ∈ N and x < 20}
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}
A = {x : x = 3p ; p ∈ N}
x = 3p
If p = 1, then x = 3 × 1 = 3
If p = 2, then x = 3 × 2 = 6
If p = 3, then x = 3 × 3 = 9
If p = 4, then x = 3 × 4 = 12
If p = 5, then x = 3 × 5 = 15
If p = 6, then x = 3 × 6 = 18
∴ A = {3, 6, 9, 12, 15, 18}
12. Find the proper subsets of {x : x2 – 9x – 10 = 0}.
Ans. x2 – 9x – 10 = 0 ⇒ x2 – 10x + x – 10 = 0
⇒ x(x – 10) + 1(x – 10) = 0 ⇒ (x – 10) (x + 1) = 0
If, (x –10) = 0 ⇒ x = 10 and, if (x + 1) = 0 ⇒ x = – 1
∴ Given set = {–1, 10}
∴ Proper subsets of this set = {–1}, {10}, {–1, 10}
13. Let ξ= {1, 2, 3, …, 9}, A = {1, 2, 3, 4, 6, 7} and B = {4, 6, 8}. Find :
