Question

Write the set $\left\{x:x=2n,nisanaturalnumber\right\}$ in roster form and description form.

Answer 1

For the given set $\left\{x:x=2n,nisanaturalnumber\right\}$

Description form:

As per the given relation, $x=2n$, where $n$ belongs to natural numbers (counting numbers from $1$to infinity) .

So putting values of $n=1,2,3,4,....$ and so on in $x=2n$, we get:

$n=1x=2\times 1=2$

$n=2x=2\times 2=4$

$n=3x=2\times 3=6$

And so on, the elements will be even natural numbers.

Hence, description form will be represented as $\left\{setofevennaturalnumbers\right\}$

Roster form:

As we have solved for the descriptive form, the elements are even natural numbers, therefore it will be infinite set.

Hence, roster form will be represented as $\left\{2,4,6,8,...\right\}$