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+12 votes
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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
asked in Theory of Computation by Veteran (59.5k points)
edited by | 1.2k views

2 Answers

+17 votes
Best answer

(b) is False. 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.

answered by Veteran (355k points)
edited by
–3 votes

(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

answered by Boss (14.2k points)
0
No. The set you gave is infinite. Any finite set is trivially regular as there are only finite number of strings. (Finite class of languages is a subset of regular class).

Your example is for (b) and that is the false statement.
+2
sorry for it.it  is a silly mistake i thought it is a very easy question so i just took any option infront of me .it happens with me at times

(b) Every subset of a regular set is regular this is false


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