Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following is true?a)All subsets ...
Start Learning for Free
Which of the following is true?
- a)All subsets of a regular set are always regular
- b)All finite subsets of non-regular set are always regular
- c)Union of two non regular set of language is not regular
- d)Infinite times union of finite set is always regular
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Which of the following is true?a)All subsets of a regular set are alwa...
None.
Most Upvoted Answer
Which of the following is true?a)All subsets of a regular set are alwa...
Explanation:
Regular set is defined as a set of strings that can be generated by a regular grammar or recognized by a finite automaton. Now, let's analyze each option to find the true statement.
Option A: All subsets of a regular set are always regular.
This statement is not true. A counterexample can be a regular set A = {a, ab}, whose subsets are A1 = {ε}, A2 = {a}, A3 = {ab}, A4 = {a, ab}. Here, A3 and A4 are not regular sets.
Option B: All finite subsets of non-regular set are always regular.
This statement is true. A non-regular language is one that cannot be generated by a regular grammar or recognized by a finite automaton. Therefore, any finite subset of a non-regular set can only contain finite strings that can be generated or recognized by a finite automaton, and hence, it is always regular.
Option C: Union of two non-regular sets of language is not regular.
This statement is not true. A counterexample can be two non-regular sets A = {a^n b^n | n ≥ 0} and B = {a^n b^n c^n | n ≥ 0}. Both these sets are not regular, but their union A ∪ B = {a^n b^n | n ≥ 0} ∪ {a^n b^n c^n | n ≥ 0} = {a^n b^n c^m | n, m ≥ 0} is a regular set.
Option D: Infinite times union of finite sets is always regular.
This statement is not true. A counterexample can be an infinite set A = {a^n | n ≥ 0}, whose finite subsets are all regular sets. But, the infinite union of all these finite subsets gives the set A itself, which is not regular. Therefore, the infinite times union of finite sets is not always regular.
Hence, the correct option is B.
Regular set is defined as a set of strings that can be generated by a regular grammar or recognized by a finite automaton. Now, let's analyze each option to find the true statement.
Option A: All subsets of a regular set are always regular.
This statement is not true. A counterexample can be a regular set A = {a, ab}, whose subsets are A1 = {ε}, A2 = {a}, A3 = {ab}, A4 = {a, ab}. Here, A3 and A4 are not regular sets.
Option B: All finite subsets of non-regular set are always regular.
This statement is true. A non-regular language is one that cannot be generated by a regular grammar or recognized by a finite automaton. Therefore, any finite subset of a non-regular set can only contain finite strings that can be generated or recognized by a finite automaton, and hence, it is always regular.
Option C: Union of two non-regular sets of language is not regular.
This statement is not true. A counterexample can be two non-regular sets A = {a^n b^n | n ≥ 0} and B = {a^n b^n c^n | n ≥ 0}. Both these sets are not regular, but their union A ∪ B = {a^n b^n | n ≥ 0} ∪ {a^n b^n c^n | n ≥ 0} = {a^n b^n c^m | n, m ≥ 0} is a regular set.
Option D: Infinite times union of finite sets is always regular.
This statement is not true. A counterexample can be an infinite set A = {a^n | n ≥ 0}, whose finite subsets are all regular sets. But, the infinite union of all these finite subsets gives the set A itself, which is not regular. Therefore, the infinite times union of finite sets is not always regular.
Hence, the correct option is B.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Top Courses for Computer Science Engineering (CSE)View all
Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer?
Question Description
Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer?.
Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following is true?a)All subsets of a regular set are always regularb)All finite subsets of non-regular set are always regularc)Union of two non regular set of language is not regulard)Infinite times union of finite set is always regularCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup