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+12 votes
1.3k views

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 (59.7k points)
edited by | 1.3k 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 (368k points)
edited by
0
example of option B)a^nb^n is non regular subset of regular (a/b)*.
–2 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 (14.4k 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
Answer:

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