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) Let A = {3, 6, 9, 12}

All objects of the set are natural numbers that are multiples of 3.

$\therefore$ A = {x : x = 3n, n $\in$ N and $1\le n\le 4$}

(ii) Let B = {2, 4, 8, 16, 32}

All objects of the set are natural numbers that are powers of 2.

$\therefore$ B = {x : x = $2^n,n\in N$ and $1\le n\le 5$}

(iii) Let C = {5, 25, 125, 625}

All objects of the set are natural numbers that are powers of 5.

$\therefore$ C = {x : x = $5^n,n\in N$ and $1\le n\le 4$}

(iv) Let D = {2, 4, 6,....}

All objects of the set are even natural numbers.

$\therefore$ D = {x : x is an even natural number}

(v) Let E = {1, 4, 9, ......., 100}

All objects of the set are perfect squares.

$\therefore$ D = {x : x = $n^2$ and $1\le n\le 10$}