Given below are two statements: one is labelled as Assertion A and the other…

2026

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: If L is regular, then its complement L' is necessarily regular.

Reason R: Complement of a language can be obtained by swapping final and non-final states in a DFA.

In the light of the above statements, choose the most appropriate answer from the options given below:

  1. Both A and R are correct and R is the correct explanation of A

  2. Both A and R are correct but R is NOT the correct explanation of A

  3. A is correct but R is not correct

  4. A is not correct but R is correct

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

Attempted by 95 students.

Show answer & explanation

Correct answer: A

Analysis of Assertion and Reason

Step 1: Analyze Assertion A. The assertion states that if a language L is regular, its complement L' is necessarily regular. This is a fundamental property of regular languages known as closure under complementation.

Step 2: Analyze Reason R. The reason states that the complement of a language can be obtained by swapping final and non-final states in a DFA. This is the standard construction method to prove closure under complementation.

Step 3: Check Relationship. Since the method described in Reason R is exactly how the property in Assertion A is proven, R is the correct explanation of A.

Conclusion: Both A and R are correct, and R is the correct explanation of A.

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