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

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In summary, the sublanguages of the language L={ε, 1, 11, 111} on Σ={0, 1} include {1}, {11}, {111}, {1, 11}, {11, 111}, {1, 11, 111}, {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}, and {ε, 1, 11, 111
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Nico
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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}?
 
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  • #2
If you wrote down the definition of sublanguage on ##\{0,1\}## more people could probably help.
 
  • #3
Nico said:
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.
 

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

The sublanguage of L={ε, 1, 11, 111} is the set of all strings that can be formed using the symbols ε, 1, 11, and 111. This includes the empty string (ε) and all possible combinations of the other symbols.

How many strings are in the sublanguage of L={ε, 1, 11, 111}?

There are 4 strings in the sublanguage of L={ε, 1, 11, 111}. These are ε, 1, 11, and 111.

What is the length of the longest string in the sublanguage of L={ε, 1, 11, 111}?

The length of the longest string in the sublanguage of L={ε, 1, 11, 111} is 3. This is the string 111.

Is the sublanguage of L={ε, 1, 11, 111} a regular language?

Yes, the sublanguage of L={ε, 1, 11, 111} is a regular language. This is because it can be described by a regular expression, which is a formal language used to represent regular languages.

How can the sublanguage of L={ε, 1, 11, 111} be generated?

The sublanguage of L={ε, 1, 11, 111} can be generated by starting with the empty string (ε) and then adding the symbols 1, 11, and 111 in any order and any number of times. This will produce all possible strings in the sublanguage.

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