Selina Concise Class 8 Math Chapter 6 Sets Exercise 6C Solutions
EXERCISE 6C
(1) Find all the subsets of each of the following sets:
(i) A = {5, 7}
Subset of set A = { }, {5}, {7}, {5, 7}
(ii) Subset of set B = { }, {a}, {b}, {c}, {a, b}, {b, C}, {c, a}, {a, b, c}
(iii) C = {x : x ∈ W, x ≤ 2} = {0, 1, 2}
Subset of set C = Ф, {0}, {1}, {2}, {0, 2}, {1, 2}, {0, 1, 2}
(iv) {P : P is a letter in the word ‘POOR’} = {p, o, r}
Subset of the given set = Ф, {p}, {o}, {r}, {p, o}, {o, r}, {p, o, r}
(2) If C is the set of letters in the word ‘cooler’, find:
(i) Set C = {c, o, l, e, r}
(ii) n (C) = 5
(iii) 25 = 2 × 2 × 2 × 2 × 2 = 32
(iv) 25 – 1 = 32 – 1 = 31
(3) T = {t, e, h}
Subset of set T = Ф, {t}, {e}, {h}, {t, e}, {e, h], {h, t}, {t, e, h}
(4) Universal set = {- 7, – 3, – 1, 0, 5, 6, 8, 9}
(i) A = {x : x < 2} = {-7, -3, – 1, 0}
(ii) B = {x : – 4 < x < 6} = {- 3, -1, 0, 5}
(5) Universal set = {x : x ∈ N and x < 20}
= {1, 2, 3, 4, 5, 6, 7, ……, 19, 20}
(i) A = {x : x = 3p; p ∈ N}
x = 3p
When, p = 1, x = 3 × 1 = 3
When, p = 2, x = 3 × 2 = 6
When, p = 3, x = 3 × 3 = 9
When, p = 4, x = 3 × 4 = 12
When, p = 5, x = 3 × 5 = 15
When, p = 6, x = 3 × 6 = 18
∴ A = {3, 6, 9, 12, 15, 18}
(ii) y = 2n + 3
When, n = 1, 2 × 1 + 3 = 5
When, n = 2, 2 × 2 + 3 = 7
When, n = 3, 2 × 3 + 3 = 9
When, n = 4, 2 × 4 + 3 = 11
When, n = 5, 2 × 5 + 3 = 13
When, n = 6, 2 × 6 + 3 = 15
∴ B = {5, 7, 9, 11, 13, 15, 17, 19}
(ii) C = {x : x is divisible by 4}
= {4, 8, 12, 16}
(6) x2 – 9x – 10 = 0
⇒ x2 – 10x + x – 10 = 0
⇒ x (x – 10) + 1 (x – 10) = 0
⇒ (x – 10) (x + 1) = 0
Either, x – 10 = 0
⇒ x = 10
Or, x + 1 = 0
⇒ x = – 1
Given set = {10, – 1}
Proper subset = Ф, {- 1}, {10}
(7) A = Triangles
B = Isosceles Triangles
C = Equilateral Triangles
(i) False, since each triangles is not isosceles triangles.
(ii) True
(iii) True, since each equilateral triangle is isosceles also
(iv) True
(v) True
(vi) True
(8) A = Quadrilaterals
B = Rectangles
C = Squares
D = Rhombuses
(i) False
(ii) False
(iii) True
(iv) True
(v) True
(vi) False
(9) Universal set = {x : x ∈ N, 10 x ≤ 35}
= {10, 11, 12, 13, ……., 34, 35}
A = {x ∈ N : x ≤ 16} = {10, 11, 12, 13, 14, 15, 16}
B = {x : x > 29} = {30, 31, 32, 33, 34, 35}
(i) A’ = {17, 18, ….., 34, 35} = {x : x ∈ N; 17 ≤ x ≤ 35}
(ii) B’ = {10, 11, 12, 13, ….., 29} = {x : x ≤ 29}