
Q2 Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces: (i) 5__A (ii) 8__A (iii) 0__A (iv) 4__A (v) 2__A (vi) 10__A Ans: (i) 5 ∈ A
(ii) 8 ∉ A
(iii) 0 ∉ A
(iv) 4 ∈ A
(v) 2 ∈ A
(vi) 10 ∉ A
Q3 Write the following sets in roster form: (i) A = {x: x is an integer and  3 < x < 7}. (ii) B = {x: x is a natural number less than 6}. (iii) C = {x: x is a twodigit natural number such that the sum of its digits is 8} (iv) D = {x: x is a prime number which is divisor of 60}. (v) E = The set of all letters in the word TRIGONOMETRY. (vi) F = The set of all letters in the word BETTER. Ans: (i) A = {x: x is an integer and –3 < x < 7}
The elements of this set are –2, –1, 0, 1, 2, 3, 4, 5, and 6 only.
Therefore, the given set can be written in roster form as
A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {x: x is a natural number less than 6}
The elements of this set are 1, 2, 3, 4, and 5 only.
Therefore, the given set can be written in roster form as
B = {1, 2, 3, 4, 5}
(iii) C = {x: x is a twodigit natural number such that the sum of its digits is 8}
The elements of this set are 17, 26, 35, 44, 53, 62, 71, and 80 only.
Therefore, this set can be written in roster form as
C = {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = {x: x is a prime number which is a divisor of 60}
2 60 2 30 3 15 5 ∴60 = 2 × 2 × 3 × 5
The elements of this set are 2, 3, and 5 only.
Therefore, this set can be written in roster form as D = {2, 3, 5}.
(v) E = The set of all letters in the word TRIGONOMETRY
There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.
Therefore, this set can be written in roster form as
E = {T, R, I, G, O, N, M, E, Y}
(vi) F = The set of all letters in the word BETTER
There are 6 letters in the word BETTER, out of which letters E and T are repeated.
Therefore, this set can be written in roster form as
F = {B, E, T, R}
Q4 Write the following sets in the setbuilder form: (i) (3, 6, 9, 12) (ii) {2, 4, 8, 16, 32} (iii) {5, 25, 125, 625} (iv) {2, 4, 6 upto infinity} (v) {1, 4, 9, upto 100} Ans: (i) {3, 6, 9, 12} = {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32}
It can be seen that 2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}.
∴ {2, 4, 8, 16, 32} = {x: x = 2^{n}, n∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625}
It can be seen that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.
∴ {5, 25, 125, 625} = {x: x = 5^{n}, n∈N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6 …}
It is a set of all even natural numbers.
∴ {2, 4, 6 …} = {x: x is an even natural number}
(v) {1, 4, 9 … 100}
It can be seen that 1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}.
∴ {1, 4, 9… 100} = {x: x = n^{2}, n∈N and 1 ≤ n ≤ 10}