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  • Math Class VIII 1 Question Bank

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    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

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    (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

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    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

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    ⇒ 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

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    (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

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    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

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    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 :