Understanding facts about regular languages, finite sets and subsets of regular languages
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05-11-2019 - |
質問
I am aware of following two facts related to two concepts: regular languages and finite sets:
- Regular languages are not closed under subset and proper subset operations.
- It is decidable whether given regular language is finite or not.
However I feel these facts are quite insufficient to prove whether following statements are true or false:
- If all proper subsets of $L$ are regular, then $L$ is regular.
- If all finite subsets of $L$ are regular, then $L$ is regular.
- If a proper subset of $L$ is not regular, then $L$ is not regular.
- Subsets of finite sets are always regular.
I feel 3 is false, as regular languages are not closed under proper subset operation. Right?
But I am unsure of the other points. What facts I am missing to answer above statements true or false?
正しい解決策はありません
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