Q78.Marks: +2.0UGC NET Paper 2: Computer Science 2nd January 2026 Shift 1
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 compliment 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✓ Correct
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
Solution
The correct answer is Both A and R are correct and R is the correct explanation of A.
Key Points
Assertion A: If L is a regular language, then its complement L' is necessarily regular. This statement is true because the complement of a regular language is always regular. Regular languages are closed under complementation.
Reason R: The complement of a language can be obtained by swapping the final and non-final states in a Deterministic Finite Automaton (DFA). This is correct as the process of complementation involves altering the accepting states of a DFA.
Since the Reason R correctly explains why the Assertion A is true, both A and R are correct, and R is the correct explanation of A.
Additional Information
Properties of Regular Languages:
Regular languages are closed under union, intersection, complementation, concatenation, and Kleene star.
Any operation performed on regular languages that maintains these closure properties will result in a regular language.
How Complementation Works in DFA:
In a DFA, the set of accepting states and non-accepting states are swapped to obtain the complement of the language.
The resulting automaton accepts all strings that the original DFA rejects and rejects all strings that the original DFA accepts.
Key Note: The process of complementing a language applies only when the language is defined over a finite alphabet and its DFA is complete (i.e., every state has a transition for every symbol in the alphabet).
