Liam from Wilbarston School sent us this well-explained solution:

Only the middle thirds of line segments are removed, so endpoints of line segments will not be removed.
Therefore, all I need to do is determine which are endpoints and which are not.

1
3

is an endpoint of C2, so it is in the Cantor set.

3
81

=
1
27

1
27

is an endpoint of C4, and therefore
3
81

is in the Cantor set.

4
9

is between
1
3

and
2
3

, thus it is in the middle third of C1 and is removed from C2 and as such isn't in the Cantor set.

4
81

is between
1
27

and
2
27

and therefore is in the middle third of C3.
It is removed from C4 and therefore does not belong.