Chapter 1 Sets

(i) 5 ∈ A

(ii) 8 ∉ A

(iii) 0 ∉ A

(iv) 4 ∈ A

(v) 2 ∈ A

(vi) 10 ∉ A

 (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 two-digit 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}

 (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 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴, and 32 = 2⁵.

∴ {2, 4, 8, 16, 32} = {x: x = 2ⁿ, n∈ N and 1 ≤ n ≤ 5}

 

(iii) {5, 25, 125, 625}

It can be seen that 5 = 5¹, 25 = 5², 125 = 5³, and 625 = 5⁴.

∴ {5, 25, 125, 625} = {x: x = 5ⁿ, 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 = 1², 4 = 2², 9 = 3² …100 = 10².

∴ {1, 4, 9… 100} = {x: x = n², n∈N and 1 ≤ n ≤ 10}