CODEWITHSUNDEEP
regular-language
southpaw93
southpaw93

Reputation: 1961

Regular language, L1 and L2

Let there be two languages L1 and L2 with the property that L1 ⊆ L2 and L2 ∈ REG then L1 ∈ REG. I have searched everywhere and I can't find anything, how do you solve this ? Can you please provide ample explanation, thank you,

Upvotes: 0

Views: 2315

Answers (1)

Patrick87
Patrick87

Reputation: 28292

I'm taking this as the question:

If L1 is a subset of L2, and L2 is regular, does it follow that L1 is regular also?

The answer is no. The proof is by counterexample. Let L2 be the following regular language: all strings over the alphabet. Let L1 be the following subset of L2: any non-regular language of the alphabet. Then L1 is a subset of L2, L2 is regular, and L1 is non-regular.

Upvotes: 1

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