Which of the following statement is false?
2025
Which of the following statement is false?
- A.
A recursive language is also a regular language
- B.
A context free language is also a regular language
- C.
A context free language is also recursive enumerable language
- D.
Both (a) and (b)
Attempted by 16 students.
Show answer & explanation
Correct answer: D
Chomsky Hierarchy Overview
The Chomsky hierarchy classifies formal languages based on their generative power. The standard inclusion relationship is: Regular Languages ⊂ Context-Free Languages ⊂ Recursive Languages ⊂ Recursively Enumerable Languages.
Regular Languages are the most restrictive.
Context-Free Languages include Regular Languages.
Recursive Languages include Context-Free Languages.
Recursively Enumerable Languages include Recursive Languages.
Option Analysis
Option A claims Recursive languages are Regular. This is false because Recursive is a superset.
Option B claims Context-Free languages are Regular. This is false because Context-Free is a superset.
Option C claims Context-Free languages are Recursively Enumerable. This is true based on the hierarchy.
Option D states both A and B are false. Since A and B are indeed false statements, this option correctly identifies the inaccuracies.
Conclusion
The question asks which statement is false. Options A and B are false statements. Option D correctly identifies that both A and B are false. Therefore, Option D is the correct answer.