Selina Concise Class 8 Math Chapter 6 Sets Exercise 6A Solutions
EXERCISE 6A
(1) Write the following sets in roster (Tabular) form:
(i) 2x + 3 = 11
⇒ 2x = 11 – 3
⇒ x = 8/2 = 4
∴ A1 = { 4 }
(ii) x2 – 4x – 5 = 0
⇒ x2 – (5 – 1)x – 5 = 0
⇒ x2 – 5x + 1x – 5 = 0
⇒ x (x – 5) + 1 (x – 5) = 0
⇒ (x + 1) (x – 5) = 0
Either, x + 1 = 0
⇒ x = – 1
Or, x – 5 = 0
⇒ x = 5
∴ A2 = {- 1, 5}
(iii) – 3 ≤ x ≤ 4
x = – 3, – 2, – 1, 0, 1, 2, 3
∴ A3 = {- 3, – 2, – 1, 0, 1, 2, 3}
(iv) x is two digit number and sum of the digits of x is 7
x = 16, 25, 34, 43, 52, 61, 70
∴ A4 = {16, 25, 34, 43, 52, 61, 70}
(v) x = 4n
∴ When, n = 0, x = 4 × 0 = 0
When, n = 1, x = 4 × 1 = 4
When, n = 2, x = 4 × 2 = 8
When, n = 3, x = 4 × 3 = 12
∴ A5 = {0, 4, 8, 12}
(2) Write the following sets in set-builder (Rule Method) form:
(i) B1 = {6, 9, 12, 15, …}
= {x : x = 3n + 3; n ϵ N}
(ii) B2 = {11, 13, 17, 19}
= {x : x is prime number between 10 and 20}
(iv) B4 = {8, 27, 64, 125, 216}
= {x : x = n3, n ϵ N and 2 ≤ n ≤ 6}
(v) B5 = {- 5, – 4, – 3, – 2, – 1}
= {x : x ϵ Z, – 5 ≤ x ≤ – 1}
(vi) B6 = {…….., – 6, – 3, 0, 3, 6, ……}
= {x : x = 3n, n ϵ Z}
(3) (i) No, 64 is not a factor of 32.
(ii) Yes, 54 is not a factor of 27.
(iii) {2, 4, 62, 124}
(iv) {1, 3, 9}
(v) {2, 3, 7, 11}
(vi) Yes
(vii) No
(4) Write the following sets in Roster form:
(i) {M, E, R, U, T}
(ii) {U, N, I, V, E, R, S, A, L}
(iii) x = y + 3, y ϵ N and y > 3
When, y = 4, x = 4 + 3 = 7
When, y = 5, x = 5 + 3 = 8
When, y = 6, x = 6 + 3 = 9
∴ A = {7, 8, 9, ….}
(iv) When, p2 = 0
⇒ p = √0 = 0
When, p2 = 1
⇒ p = √1 = 1
When, p2 = 4
⇒ p = √4 = 2
When, p2 = 9
⇒ p = √6 = 3
When, p2 = 16
⇒ p = √16 = 4
∴ B = {0, 1, 2, 3, 4}
(v) C = {x : x is composite number and 5 ≤ x ≤ 21}
5 ≤ x ≤ 21 means x = 5, 6, 7, 8, ….., 20, 21
But we are given that x is composite number
∴ x = 6, 8, 9, 10, 11, ….., 19, 20, 21
∴ Roster form of the given set C = {6, 8, 9, 10, ….., 21}
(5) List the elements of the following sets:
(i) x2 – 2x – 3 = 0
⇒ x2 – 3x + x – 3 = 0
⇒ x (x – 3) + 1 (x – 3) = 0
⇒ (x + 1) (x – 3) = 0
Either, x + 1 = 0
⇒ x = – 1
Or, x – 3 = 0
⇒ x = 3
Elements of the set are 3 and – 1.
(ii) x = 2y +5 , y ϵ N and 2 ≤ y ≤ 6
When, y = 2, x = 4 + 5 = 9
When, y = 3, x = 6 + 5 = 11
When, y = 4, x = 8 + 5 = 13
When, y = 5, x = 10 + 5 = 15
Elements of the set are 9, 11, 13, 15.
(iii) x is a factor of 24
24 = 1 × 24
24 = 2 × 12
24 = 3 × 8
24 = 2 × 12
24 = 4 × 6
Elements of the set are 1, 2, 3, 4, 6, 8, 12, 24.
(iv) x ϵ Z and x2 ≤ 4
When, x2 = 4
⇒ x = √4 = 2
When, x2 = 1
⇒ x = √1 = 1
When, x2 = 0
⇒ x = √0 = 0
Elements of the set are -2, -1, 0, 1, 2
(v) 3x – 2 ≤ 10
⇒ 3x ≤ 10 + 2
⇒ 3x ≤ 12
⇒ x ≤ 12/3
⇒ x ≤ 4
Elements of the set are 1, 2, 3, 4.
(vi) 4 – 2x > – 6, x ∈ Z
⇒ 4 – 2x > – 6
⇒ – 2x > – 6 – 4
⇒ – 2x > – 10
⇒ 2x > 10
⇒ x > 10/2
⇒ x > 5
Elements of the set are 6, 7, 8, ….., 0, – 1…….