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) $\{3,6,9,12\}$
$=\{x:x=3n,nϵN$ and $1\le n\le 4\}$

Alternatively, $\{x:x\text{is a multiple of 3 and}x\le 12\}$
(ii) $\{2,4,8,16,32\}$
It can be seen that $2=2^1,4=2^2,8=2^3,16=2^4$, and $32=2^5$.
$\therefore \{2,4,8,16,32\}=\{x:x=2^n,nϵN$ and $1\le n\le 5\}$
(iii) $\{5,25,125,625\}$
It can be seen that $5=5^1,25=5^2,125=5^3$, and $625=5^4$.
$\therefore \{5,25,125,625\}=\{x:x=5^n,nϵN$ and $1\le n\le 4\}$
(iv) $\{2,4,6,....\}$
It is a set of all even natural numbers.
$\therefore \{2,4,6,....\}=\{x:x\text{is an even natural number}\}$
(v) $\{1,4,9,.....100\}$
$\therefore \{1,4,9...100\}=\{x:x=n^2,nϵN$ and $1\le n\le 10\}$

Alternatively, $\{x:x\text{is a square of natural number and}x\le 100\}$