Question

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

(i) $\{3,6,9,12,15\}$

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

$\text{Given set:}\{3,6,9,12,15\}$

$\text{As,}$

$3=3\times 1$

$6=3\times 2$

$9=3\times 3$

$12=3\times 4$

$15=3\times 5$

So, we can see that the elements of given set are multiples of 3 between 2 and 16.

Hence, the set builder form of the given set is
$\{x:x\text{is a multiple of 3 and 2 < x < 16}\}.$