Question

State, whether each of the following sets is a finite set or an infinite set:

$\text{{}x:x=3n-2,n\in Z,n\le 8\text{}}$

Answer 1

Step: Check whether the given set is a finite set or an infinite set
We know that,
Finite sets are the sets having a finite/countable number of members.

Infinite sets are the sets having an infinite/uncountable number of members.
Given, {$\text{{}x:x=3n-2,n\in Z,n\le 8\text{}}$
As, $n\le 8$ and n $\in Z$

$\Rightarrow n=\text{{.......-2,-1,0,1,2,3,4,5,6,7,8}}$
Which are uncountable (infinite) number of elements.

Corresponding to infinite number of values of $n$, we will infinite values of
$x(\because x=3n-2).$

So, the set will have infinite elements.
Hence, the set $\text{{}x:x=3n-2,n\in Z,n\le 8\text{}}$ is an infinite set.