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Which of the following statements is false?

  1. Every finite subset of a non-regular set is regular
  2. Every subset of a regular set is regular
  3. Every finite subset of a regular set is regular
  4. The intersection of two regular sets is regular
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3 Answers

Best answer
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Correct Option: B

Any language is a subset of $\Sigma^*$ which is a regular set. So, if we take any non-regular language, it is a subset of a regular language.

(a) and (c) are regular as any finite language is regular.

(d) is regular as regular set is closed under intersection.

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B is false because if u take a*b* as an example a^n b^n is a subset of a*b* but its not regular
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(c) Every finite subset of a regular set is regular this is false

example:a^n b^n from regular set (a+b)* is not regular

Answer:

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