What is the sublanguage of L={ε, 1, 11, 111}

[Nico]

TL;DR Summary: [Formal languages and automata]
Show all sublanguages of the language L={ε, 1, 11, 111} on Σ={0, 1}.

[Formal languages and automata]
Show all sublanguages of the language L={ε, 1, 11, 111} on Σ={0, 1}.

Is the answer {1}, {11}, {111}, {1, 11}, {11, 111}, {1, 11, 111}?

Or {ε}, {ε, 1}, {ε, 11}, {ε, 111}, {1, 11}, {1, 111}, {11, 111}, {ε, 1, 11}, {ε, 1, 111}, {ε, 11, 111}, {1, 11, 111}?

 

[Office_Shredder]

If you wrote down the definition of sublanguage on $\{0,1\}$ more people could probably help.

 

[Steve4Physics]

Is the answer {1}, {11}, {111}, {1, 11}, {11, 111}, {1, 11, 111}?

Or {ε}, {ε, 1}, {ε, 11}, {ε, 111}, {1, 11}, {1, 111}, {11, 111}, {ε, 1, 11}, {ε, 1, 111}, {ε, 11, 111}, {1, 11, 111}?

In my limited understanding (from a long time ago), ε (the empty string) is just as valid as any other string.

So I’d say your first approach is incomplete and your second approach is correct.

However, I think you have some mistakes. The ones I spotted are:
You missed out {1, 111} from your first answer.
You missed out {ε,1, 11, 111} from your second answer.

There may be other omissions – I only checked quickly.