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ICSE-VIII-Mathematics

06: Sets Class 8 Maths

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    Section : A
  • Qstn #1
    Write the following sets in roster (Tabular) form :
  • #1-i
    A1 = {x : 2x + 3 = 11}
    Ans : A1 = {x : 2x + 3 = 11}
    ∴ 2x + 3 = 11
    ⇒ 2x = 11 - 3
    ⇒ 2x = 8
    ⇒ x = 8/2 ⇒ x = 4
    ∴ Given set in roster (Tabular) form is
    A1 = {4}
  • #1-ii
    A2 = {x : x2 - 4x - 5 = 0}
    Ans : A2 = {x : x2 - 4x - 5 = 0}
    ∴ x2 - 4x - 5 = 0
    ⇒ x2 - 5x + x - 5 = 0
    ⇒ x(x - 5) + 1(x - 5) =0
    ⇒ (x - 5)(x + 1) = 0
    ∴ Either x - 5 = 0 or x + 1 = 0
    ⇒ x = 5 ⇒ x = -1
    ∴ Given set in roster (Tabular) form is A2 = {5, -1}
  • #1-iii
    A3 = {x : x ∈ Z, -3 ≤ x < 4}
    Ans : A3 = {x : x ∈ Z, -3 ≤ x < 4}
    ∵ -3 ≤ x < 4
    ∴ x = -3, -2, -1, 0, 1, 2, 3
    ∴ Given set in roster (Tabular) form is
    A3 = {-3, -2, -1, 0, 1, 2, 3}
  • #1-iv
    A4 = {x : x is a two digit number and sum of digits of x is 7}
    Ans : A4 = {x : x is a two digit number and sum of digits of x is 7}
    ∵ x is a two digit number and sum of digits of x is 7
    ∴ x = 16, 25, 34, 43, 52, 61, 70
    ∴ Given set in roster (Tabular) form is
    A4 = {16, 25, 34, 43, 52, 61, 70}
  • #1-v
    A5 = {x : x = 4n, n ∈ W and n < 4}
    Ans : A5 = {x : x = 4n, n ∈ W and n < 4}
    ∵ x = 4n
    ∴ When n = 0, x = 4 × 0
    ⇒ x = 0
    When n = 1, x = 4 × 1
    ⇒ x = 4
    When n = 2, x = 4 × 2
    ⇒ x = 8
    When n = 3, x = 4 × 3
    ⇒ x = 12
    ∴ Given set in roster (Tabular) form is
    A5 = {0, 4, 8, 12}
  • #1-vi
    A6 = {x : x = n/(n + 2) ; n ∈ N and n > 5}
    Ans : A6 = {x : x = n/(n + 2); n ∈ N & n > 5}
    ∵ x = n/(n + 2)
    ∴ When n = 6, x = 6/(6 + 2)
    ⇒ x = 6/8⇒ x = ¾
    When n = 7, x = 7/(7 + 2)⇒ x = 7/9
    When n = 8, x = 8/(8 + 2)⇒ x = 8/10
    ⇒ x = 4/5
    When n = 9, x = 9/(9 + 2)⇒ x = 9/11
    ∴ Given set in roster (Tabular) form is
    A6 = {3/4, 7/9, 4/5, 9/11,...}
  • Qstn #2
    Write the following sets in set-builder (Rule Method) form:
  • #2-i
    B1 = {6, 9, 2, 15, ...}
    Ans : B1 = {6, 9, 12, 15, ....}
    = {x : x = 3n + 3; n ∈ N}
  • #2-ii
    B2 = {11, 13, 17, 19 }
    Ans : B2 = {11, 13, 17, 19}
    = {x : x is a prime number between 10 and 20}
  • #2-iii
    B3 = (1/3, 3/5, 5/7, 7/9, 9/11,...}
    Ans : B3 = {1/3, 3/5, 5/7, 7/9, 9/11, ...}
    = {x : x = n/(n + 2), where n is an odd natural number}
  • #2-iv
    B4 = {8, 27, 64, 125, 216}
    Ans : B4 = {8, 27, 64, 125, 216}
    = {x : x = n3; n ∈ N and 2 ≤ n ≤ 6}
  • #2-v
    B5 = {-5, -4, -3, -2, -1}
    Ans : B5 = {-5, -4, -3, -2, -1}
    = {x : x ∈ Z, -5 ≤ x ≤ -1}
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