Closure properties MCQs

By: Prof. Dr. Fazal Rehman | Last updated: September 23, 2024

Closure Properties of Regular Languages Regular languages are closed under which of the following operations? A) Union B) Intersection C) Complement D) All of the above Answer: D Which of the following operations on regular languages always results in a regular language? A) Concatenation B) Kleene star C) Reversal D) All of the above Answer: D If L1 and L2 are regular languages, then L1 ∪ L2 is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily regular Answer: A Regular languages are closed under the following operation except: A) Complement B) Homomorphism C) Intersection with a context-free language D) Inverse homomorphism Answer: C If L is a regular language, then the complement of L is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily regular Answer: A Which of the following is not a closure property of regular languages? A) Subtraction B) Union C) Intersection D) Kleene star Answer: A The intersection of a regular language with any other regular language is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily regular Answer: A Regular languages are not closed under: A) Union B) Concatenation C) Complement D) Infinite intersection Answer: D Given two regular languages L1 and L2, their concatenation L1L2 is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily regular Answer: A If L1 is a regular language and L2 is a finite language, their intersection L1 ∩ L2 is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily regular Answer: A Closure Properties of Context-Free Languages Context-free languages are closed under which of the following operations? A) Union B) Concatenation C) Kleene star D) All of the above Answer: D Which of the following operations on context-free languages does not necessarily result in a context-free language? A) Union B) Intersection with a regular language C) Intersection with another context-free language D) Kleene star Answer: C If L1 and L2 are context-free languages, then L1 ∪ L2 is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily context-free Answer: B The concatenation of two context-free languages is: A) Always regular B) Always context-free C) Always context-sensitive D) Not necessarily context-free Answer: B Context-free languages are not closed under: A) Union B) Concatenation C) Intersection D) Kleene star Answer: C If L is a context-free language, the language L (Kleene star) is:* A) Regular B) Context-free C) Context-sensitive D) Not necessarily context-free Answer: B If L1 is a context-free language and L2 is a regular language, their intersection L1 ∩ L2 is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily context-free Answer: B Which of the following is not a closure property of context-free languages? A) Union B) Concatenation C) Complement D) Kleene star Answer: C The complement of a context-free language is: A) Always context-free B) Always context-sensitive C) Not necessarily context-free D) Always regular Answer: C If L1 and L2 are context-free languages, the language L1 – L2 (difference) is: A) Context-free B) Regular C) Context-sensitive D) Not necessarily context-free Answer: D Context-free languages are closed under the following operations except: A) Reversal B) Homomorphism C) Inverse homomorphism D) Complement Answer: D The union of a context-free language and a regular language is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily context-free Answer: B Which of the following statements is true regarding context-free languages? A) They are closed under intersection with regular languages. B) They are closed under intersection with other context-free languages. C) They are closed under complement. D) They are not closed under union. Answer: A If L1 is a context-free language and L2 is a regular language, their concatenation L1L2 is: A) Regular B) Context-free C) Context-sensitive D) Not necessarily context-free Answer: B  

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