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

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(i) {3, 6, 9, 12}

The given set can be written in the set-builder form as {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

(ii) {2, 4, 8, 16, 32}

We know that 2 = 2^1, 4 = 2^2, 8 = 2^3, 16 = 2^4, and 32 = 2^5.

Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}.

(iii) {5, 25, 125, 625}

We know that 5 = 5^1, 25 = 5^2, 125 = 5^3, and 625 = 5^4.

Therefore,

the given set {5, 25, 125, 625} can be written in the set-builder form as {x: x = 5^n, n ∈N and 1 ≤ n ≤ 4}.

(iv) {2, 4, 6 …}

{2, 4, 6 …} is a set of all even natural numbers

Therefore,

the given set {2, 4, 6 …} can be written in the set-builder form as {x: x is an even natural number}.

(v) {1, 4, 9 … 100}

We know that 1 = 1^2, 4 = 2^2, 9 = 3^2 …100 = 10^2.

Therefore,

the given set {1, 4, 9… 100} can be written in the set-builder form as {x: x = n^2, n ∈ N and 1 ≤ n ≤ 10}.

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Answer 2

Answer:

(i) {3, 6, 9, 12}

The given set can be written in the set-builder form as {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

(ii) {2, 4, 8, 16, 32}

We know that 2 = 2^1, 4 = 2^2, 8 = 2^3, 16 = 2^4, and 32 = 2^5.

Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {x: x = 2n, n ∈ N and 1 ≤ n ≤ 5}.

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

We know that 5 = 5^1, 25 = 5^2, 125 = 5^3, and 625 = 5^4.

Therefore,

the given set {5, 25, 125, 625} can be written in the set-builder form as {x: x = 5^n, n ∈N and 1 ≤ n ≤ 4}.

(iv) {2, 4, 6 …}

{2, 4, 6 …} is a set of all even natural numbers

Therefore,

the given set {2, 4, 6 …} can be written in the set-builder form as {x: x is an even natural number}.

(v) {1, 4, 9 … 100}

We know that 1 = 1^2, 4 = 2^2, 9 = 3^2 …100 = 10^2.

Therefore,

the given set {1, 4, 9… 100} can be written in the set-builder form as {x: x = n^2, n ∈ N and 1 ≤ n ≤ 10}.