06: Sets Class 8 Maths : Icse-viii-mathematics

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ICSE-VIII-Mathematics

06: Sets Class 8 Maths

with Solutions - page 2

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#2-vi
B₆ = {..., -6, -3, 0, 3, 6 ....}
Ans : B₆ = {..., -6, -3, 0, 3, 6, ...}
= {x : x = 3n, n ∈ Z}

#3

#3-i
Is {1, 2, 4, 16, 64} = {x : x is a factor of 32} ? Give reason.
Ans : No, {1, 2, 4, 16, 64} ≠ {x : x is a factor of 32}
Because 64 is not a factor of 32

#3-ii
Is {x : x is a factor of 27} ≠ {3, 9, 27, 54}? Give reason.
Ans : Yes, { x : x is a factor of 27} + {3, 9, 27, 54}
Because 54 is not a factor of 27

#3-iii
Write the set of even factors of 124.
Ans : 1 × 124 = 124
2 × 62 = 124
4 × 31 = 124
Factors of 124 = 1, 2, 4, 31, 62, 124
Set of even factors 124 = {2, 4, 62, 124}

#3-iv
Write the set of odd factors of 72.
Ans : 1 × 172 = 72
2 × 36 = 72
3 × 24 = 72
4 × 18 = 72
6 ×12 = 72
8 × 9 = 72
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Set of odd factors of 72 = {1, 3, 9}

#3-v
Write the set of prime factors of 3234.
Ans :
3234 = 2 × 3 × 7 × 7 × 11
∴ Set of prime factors of 3234 = {2, 3, 7, 11}

#3-vi
Is {x : x² - 7x + 12 = 0} = {3, 4} ?
Ans : x² - 7x + 12 = 0
⇒ x² - 4x - 3x + 12 = 0
⇒ x(x - 4) - 3(x - 4) = 0
⇒ (x - 4)(x - 3) = 0
∴ Either x - 4 = 0 or x - 3 = 0
⇒ x = 4 ⇒ x = 3
∴ {x : x² - 7x + 12 = 0} = {3, 4} is true

#3-vii
Is {x : x² - 5x - 6 = 0} = {2, 3} ?
Ans : x² - 5x - 6 = 0
⇒ x² - 6x + x - 6 = 0
⇒ x(x - 6) + 1(x - 6) = 0
⇒ (x - 6)(x + 1) = 0
∴ Either x - 6 = 0 or x + 1 = 0
i.e., x = 6 i.e., x = -1
∴ {x : x² - 5x - 6 = 0} ≠ {2, 3}
In other words {x : x² - 5x - 6 = 0} = {2, 3} is not true

Qstn #4
Write the following sets in Roster form:

#4-i
The set of letters in the word ‘MEERUT’.
Ans : Roster form of the set of letters in the word “MEERUT” = {m, e, r, u, t}

#4-ii
The set of letters in the word ‘UNIVERSAL’.
Ans : Roster form of the set of letters in the word “UNIVERSAL” = {u, n, i, v, e, r, s, a, l}

#4-iii
A = {x : x = y + 3, y ∈ N and y > 3}
Ans : A = {x : x = y + 3, y ∈ N and y > 3}
x = y + 3
when y = 4, x = 4 +3 = 7
when y = 5, x = 5 + 3 = 8
when y = 6, x = 6 + 3 = 9
when y = 7, x = 7 + 3 = 10
when y = 8, x = 8 + 3 = 11
∴ Roster form of the given set A = {7, 8, 9, 10, 11 ......}

#4-iv
B = {p : p ∈ W and p² < 20}
Ans : B = {P : P ∈ W and p² < 20}
When P² = 0
P = √0 = 0
When P² = 1
P = √1 = 1
When P² = 4
P = √4 = 2
When P² = 9
P = √9 = 3
When P² = 16
P = √16 = 4
∴ Roster form of the given set B = {0, 1, 2, 3, 4}

#4-v
C = {x : x is composite number and 5 < x < 21}
Ans : C = {x : x is composite number and 5 ≤ x ≤ 21}
5 ≤ x ≤ 21 means x = 5, 6, 7, 8, 9, 10, ......, 21
But we are given that x is a composite number
∴ x = 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21
∴ Roster form of the given set C = {6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21}
Note: Composite numbers: The natural numbers (greater than 1), which are not prime, are called composite numbers.