Question

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

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

Answer 1

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

Inifinite sets are the having an infinite/uncountable number of members

As $n\le 8$ and $n\in W$

$\Rightarrow n=\text{{0,1,2,3,4,5,6,7,8}}$

Corresponding value of $x$ will be for

$n=0\Rightarrow x=3\left(0\right)-2=0-2=-2$

$n=1\Rightarrow x=3\left(1\right)-2=3-2=1$

$n=2\Rightarrow x=3\left(2\right)-2=6-2=4$

$n=3\Rightarrow x=3\left(3\right)-2=9-2=7$

$n=4\Rightarrow x=3\left(4\right)-2=12-2=10$

$n=5\Rightarrow x=3\left(5\right)-2=15-2=13$

$n=6\Rightarrow x=3\left(6\right)-2=18-2=16$

$n=7\Rightarrow x=3\left(7\right)-2=21-2=19$

Thus, the values of $x$ are
$\text{{-2,1,4,7,10,13,16,19,22}}$

Therefore, the set is finite.

Hence, the set $\text{{}x:x=3n-2,n\in W\text{,}n\le 8\text{}}$ is a finite set.