Write the following sets in the set-builder form

(i) Given that,

{3, 6, 9, 12}

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set are multiple of 3 from 1 to 4 

such that {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

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

(ii) Given that,

{2, 4, 8, 16, 32}

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set are powers of 2 from 1

to 5 such that {x: x = 2ⁿ, n ∈ N and 1 ≤ n ≤ 5}

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

(iii) Given that,

{5, 25, 125, 625} 

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set are powers of 5 from 1 to 4 

such that {x: x = 5ⁿ, n ∈N and 1 ≤ n ≤ 4}.

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

(iv) Given that,

{2, 4, 6 …}

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers are the set of all even natural numbers.

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

(v) Given that,

{1, 4, 9 … 100}

To represent the given set in the set builder form

In set builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.

From the given set, we observe that the numbers in the set squares of numbers form1 to 10 

such that {x: x = n², n ∈ N and 1 ≤ n ≤ 10}.

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