Question

form:
(i) A4 = {x: 2+3 = 11}
(ii) Az = {x : x2 - 4x - 5 = 0}
A,
(iv) Write the set
(v) Write the set
(vi) Is (x:x2-7
(vii) Is x X2 - 5
2}​

Answer 1

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,……}