Write the following sets in the set-builder form :
(i) (3, 6, 9, 12} (ii) {2,4,8,16,32} (iii) {5, 25, 125, 625}
(iv) {2, 4, 6, . . .} (v) {1,4,9, . . .,100}

Solution:

(i) {3, 6, 9,12}

We see that

•  3 = 3 x 1
•  6 = 3 x 2
•  9 = 3 x 3
•  12 = 3 x 4

Therefore, the set builder form of the given set is,

{3, 6, 9, 12} = {x : x = 3n, n ∈ N and 1 ≤ n ≤ 4}

(ii) {2, 4, 8, 16, 32}

We see that

• 2 = 2¹
• 4 = 2²
• 8 = 2³
• 16 = 2⁴
• 32 = 2⁵

Therefore, the set builder form of the given set is,

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

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

We see that

• 5 = 5¹
• 25 = 5²
• 125 = 5³ 
• 625 = 5⁴

Therefore, the set builder form of the given set is,

{5, 25, 125, 625} = {x : x = 5ⁿ , n ∈ N and 1 ≤ n ≤ 4}

(iv) {2, 4, 6....}

We see that it is a set of all even natural numbers.

Therefore,

{2, 4, 6....} = {x : x is an even natural number}

(v) {1, 4, 9.....100}

We see that

• 1 = 1²
• 4 = 2²
• 9 = 3²
• .....100 = 10²

Therefore, the set builder form of the given set is,

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

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NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.1 Question 4

Write the following sets in the set-builder form : (i) (3, 6, 9, 12} (ii) {2,4,8,16,32} (iii) {5, 25, 125, 625} (iv) {2, 4, 6, . . .} (v) {1,4,9, . . .,100}

Summary:

We are asked to find the set-builder form of the given sets. We found that
(i) {3, 6, 9, 12} = {x : x = 3n, n ∈ N and 1 ≤ n ≤ 4}
(ii) {2, 4, 8, 16, 32} = {x : x = 2ⁿ , n ∈ N and 1 ≤ n ≤ 5}
(iii) {5, 25, 125, 625} = {x : x = 5ⁿ , n ∈ N and 1 ≤ n ≤ 4}
(iv) {2, 4, 6....} = {x : x is an even natural number}
(v) {1, 4, 9.....100} = {x : x = n², n ∈ N and 1 ≤ n ≤ 10}