Question

Write the set $O=\left\{x:x=2n-1forn\in N\right\}$ in descriptive form.

Answer 1

In descriptive form, we describe the elements of the set.

The element of set $O$ are in the form of $x=2n-1$, where $n\in N$, natural numbers.

So $n$will take the values as $1,2,3,4....$

putting $n=1$ in $x=2n-1$, we get $x=2\times 1-1=1$

putting $n=2$ in $x=2n-1$, we get $x=2\times 2-1=3$

putting $n=3$ in $x=2n-1$, we get $x=2\times 3-1=5$

Therefore, the elements in set will be odd natural numbers.

Hence in descriptive form it can be represented as $O=Setofalloddnaturalnumbers=\left\{Oddnaturalnumbers\right\}$