Question

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} 

Answer 1

(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}