Closure relations of a language

[JimmyK]

Hi, I'm having a little trouble understand the idea of closure as so many places seem to describe it differently.

I'm working on an example problem that states "L* is the closure of language L under which relations?"

From what I gather, for a language to be closed over a relation, it means that applying that relation to any of its elements results in an element that is also in the language. Is this a correct understanding of the term?

Applying this knowledge to that question, I would think the answers are:
Union: L U L is in L*
Concatenation: LL is in L*
Kleene Star: L* is in L*

Is this line of reasoning correct, or am I totally missing the mark? Thanks in advance.

 

[Valkarie]

Yes, your understanding of closure is correct. And your reasoning is also correct. Yes, union, concatenation and Kleene Star will be the relations that will be used to create the closure of language L.