Question

Write the following sets in the set-builder form:
$\left(i\right)$ $\{3,6,9,12\}$
$\left(ii\right)$ $\{2,4,8,16,32\}$
$\left(iii\right)$ $\{5,25,125,625\}$
$\left(iv\right)$ $\{2,4,6,....\}$
$\left(v\right)$ $\{1,4,9,....,100\}$

Answer 1

$\left(i\right)$$\because 3=3\times 1,6=3\times 2,9=3\times 3$ and $12=3\times 4$
So, given set can be written in the set builder form as
$\{x:x=3n,n\in N\text{and}1\le n\le 4\}$

$\left(ii\right)$$\because 2^1=2,2^2=4,2^3=8,2^4=16\text{and}{2}^5=32$
So, given set can be written in the set builder form as
$\{x:x=2^n,n\in N\text{and}1\le n\le 5\}$

$\left(iii\right)$$\because 5^1=5,5^2=25,5^3=125\text{and}{5}^4=625$
So, given set can be written in the set builder form as
$\{x:x=5^n,n\in N\text{and}1\le n\le 4\}$

$\left(iv\right)$Given: set $\{2,4,6,...\}$ is a set of all even natural numbers.
So, given set can be written in the set builder form as
$\{x:x=2n\text{and}n\in N\}$

$\left(v\right)$$\because 1^2=1,2^2=4,3^2=9,4^2=16,....,{10}^2=100$
So, given set can be written in the set builder form as
$\{x:x=n^{2}n\in N\text{and}1\le n\le 10\}$