NCERT Solutions
Class 11 Maths
Sets

Ex.1.1 Q.4
Write the following sets in the set-builder form:
(1) (3, 6, 9, 12)
(2) {2, 4, 8, 16, 32}
(3) {5, 25, 125, 625}
(4) {2, 4, 6 ...}
(5) {1, 4, 9 ... 100}
(1) {3, 6, 9, 12} = {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}
(2) {2, 4, 8, 16, 32}
It can be seen that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.
So, {2, 4, 8, 16, 32} = {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}
(3) {5, 25, 125, 625}
It can be seen that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.
So, {5, 25, 125, 625} = {x: x = 5n, n ∈ N and 1 ≤ n ≤ 4}
(4) {2, 4, 6 ...}
It is a set of all even natural numbers.
So, {2, 4, 6 ...} = {x: x is an even natural number}
(5) {1, 4, 9 ... 100}
It can be seen that 1 = 12, 4 = 22, 9 = 32, ......., 100 = 102.
So, {1, 4, 9... 100} = {x: x = n2, n ∈ N and 1 ≤ n ≤ 10}