Closure properties MCQs

By: Prof. Dr. Fazal Rehman Shamil | 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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