Question

Write the set $\left\{x:x=2n-1,nisanaturalnumber\right\}$ in roster form and description form.

Answer 1

For the set $\left\{x:x=2n-1,nisanaturalnumber\right\}$

Description form:

As per the given relation, $x=2n-1$, 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 $x=2n-1$, we get:

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

$n=2x=2\times 2-1=3$

$n=3x=2\times 3-1=5$

and so on, the elements will be odd natural numbers.

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

Roster form:

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

Hence, roster form will be represented as $\left\{1,3,5,7,...\right\}$