Qstnid -A-4- Write The Following Sets In Roster Form: (I) The Set Of Letters In The Word &Lsquo;meerut’. (Ii) The Set Of Letters In The Word &Lsquo;universal’. (Iii) A = {X : X = Y + 3, Y ∈ N And Y &Gt; 3} (Iv) B = {P : P ∈ W And P<sup>2</sup> &Lt; 20} (V) C = {X : X Is Composite Number And 5 &Lt; X &Lt; 21} - 06: Sets Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

06: Sets Class 8 Maths

with Solutions - page 2

Qstn# A-4 Prvs-Qstn Next-Qstn

#4
Write the following sets in Roster form: (i) The set of letters in the word ‘MEERUT’. (ii) The set of letters in the word ‘UNIVERSAL’. (iii) A = {x : x = y + 3, y ∈ N and y > 3} (iv) B = {p : p ∈ W and p² < 20} (v) C = {x : x is composite number and 5 < x < 21}
Ans : (i) Roster form of the set of letters in the word “MEERUT” = {m, e, r, u, t} (ii) Roster form of the set of letters in the word “UNIVERSAL” = {u, n, i, v, e, r, s, a, l} (iii) 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 ......} (iv) 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} (v) 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.

#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.