# 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 = 2
^{1} - 4 = 2
^{2} - 8 = 2
^{3} - 16 = 2
^{4} - 32 = 2
^{5}

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

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

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

We see that

- 5 = 5
^{1} - 25 = 5
^{2} - 125 = 5
^{3} - 625 = 5
^{4}

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

{5, 25, 125, 625} = {x : x = 5^{n} , 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 = 1
^{2} - 4 = 2
^{2} - 9 = 3
^{2} - .....100 = 10
^{2}

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

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

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 = 2^{n} , n ∈ N and 1 ≤ n ≤ 5}

(iii) {5, 25, 125, 625} = {x : x = 5^{n} , 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}