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, {{x:x=3n−2,n∈Z,n≤8}
As, n≤8 and n ∈Z
⇒ n={.......-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 (∵x=3n−2).
So, the set will have infinite elements.
Hence, the set {x:x=3n−2,n∈Z,n≤8} is an infinite set.