Write the following sets in the set-builder form

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
(i) {3, 6, 9, 12} here each element is multiple of 3 and each element is a natural number and number are between 2 and 13
Hence set {3, 6, 9, 12} } can be written in set builder form as {x: x is natural number between 2 and 13 and multiple of 3}
Or we can write answer as
Hence set {3, 6, 9, 12} } can be written in set builder form as {x: x = 3n, n∈ N and 1 ≤ n ≤ 4}

(ii) {2, 4, 8, 16, 32}
It can observe that 2 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴, and 32 = 2⁵.
Hence set {2, 4, 8, 16, 32} can be written in set builder form as {x: x = 2ⁿ, n∈ N and 1 ≤ n ≤ 5}


(iii) {5, 25, 125, 625}
It can be observe that 5 = 5¹, 25 = 5², 125 = 5³, and 625 = 5⁴.
Hence set {5, 25, 125, 625} can be written in set builder form as {x: x = 5ⁿ, n∈N and 1 ≤ n ≤ 4}

(iv) {2, 4, 6 …}
It is a set of all even natural numbers.
Hence set {2, 4, 6 …} can be written in set builder form as {x: x is an even natural number}

(v) {1, 4, 9 … 100}
It can be observe that 1 = 1², 4 = 2², 9 = 3² …100 = 10²
Hence set {1, 4, 9… 100} …} can be written in set builder form as {x: x = n², n∈N and 1 ≤ n ≤ 10}