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Question: ($B$ and $C$ are languages) $B$ is finite,$C$ isn't regular:

Prove/Disprove: $C\cup B$ isn't regular.

Thoughts: My intuition says this is true, but I need an idea to prove it. Since I don't know if $C$ as a CFG or RE language I don't know what kind of machine I can build for it.

Raphael
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jreing
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1 Answers1

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Hint 1: Try to prove the contrapositive, namely: if $C\cup B$ is regular and $B$ is finite, then $C$ is regular.

Hint 2: Use closure properties of regular languages.

Dave Clarke
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