A¹ ={x:2x + 3 = 11} in tabular form
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Answer:
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Step-by-step explanation:
(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}
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Answer:
like this (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 >
answer:(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,……}
Step-by-step explanation:
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