Question

Express each of the follwing sets in set-builder notation (form):

(iii) $\{1,4,9,16,25,36\}$

Answer 1

Step: Expressing the given set in set-builder form

In set builder method the actual elements of the set are not written, but a rule or a statement or a formula is written in the briefest possible way

$\text{Given set}=\{1,4,9,16,25,36\}$

$\text{As}$, $1=1^2$

$4=2^2$

$9=3^2$

$16=4^2$

$25=5^2$

$36=6^2$

We can see that the elements of given set are squares of the first 6 natural numbers.

Hence, the set builder form of the given set is
$\{x:x\text{is a square of the first 6 natural numbers}\}$.