Question
Download Solution PDFConsider R to be any regular language and L1, L2 be any two context-free languages Which one of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Context-free languages are closed under union and difference but not closed under complementation and intersection.
Explanation:
Option 1: (L1 ∪ L2)’ – R
As context-free languages are closed under union and set difference but not under complementation. Therefore (L1 ∪ L2)’ is not a context-free language and hence (L1 ∪ L2)’ – R is also not a context-free
Option 2: L1 – R is context-free
Every regular language is also closed under context-free language and the set difference of a context-free language from Regular Language is context-free. So, it is correct.
Option 3: L’1 is context-free
L1 is a context-free language. According to the property, its complement can’t be context-free.
Option 4: L1 ∩ L2 is context-free
It violated the context-free language property. The intersection of two CFL’s is not CFL. So, it is incorrect.
Last updated on Jun 19, 2025
-> The UGC NET City Slip 2025 has been released on its official website today.
-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.
-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.
-> The exam is conducted bi-annually - in June and December cycles.
-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions.
-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.