Qstnid -A-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 &Le; X &Lt; 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 &Lt; 4} (Vi) A6 = {X : X = N/(n + 2) ; N ∈ N And N &Gt; 5} - 06: Sets Class 8 Maths

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ICSE-VIII-Mathematics

06: Sets Class 8 Maths

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Qstn# A-1 Prvs-Qstn Next-Qstn

#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 = n/(n + 2) ; n ∈ N and n > 5}
Ans : (i) 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} (ii) 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} (iii) 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} (iv) 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} (v) 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} (vi) 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,...}

#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,...}