Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following statements is false?a)...
Start Learning for Free
Which of the following statements is false?
- a)Every finite subset of a non-regular set is regular
- b)Every subset of a regular set is regular
- c)Every finite subset of a regular set is regular
- d)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a ...
Any language is a subset of ∑* which is a regular set. So, if we take any non-regular language, it is a subset of a regular language.
(a) and (c) are regular as any finite language is regular.
(d) is regular as regular set is closed under intersection.
Most Upvoted Answer
Which of the following statements is false?a)Every finite subset of a ...
False Statement: Every subset of a regular set is regular.
Explanation:
To understand why this statement is false, we need to have a clear understanding of what a regular set is.
Regular Set:
In formal language theory, a regular set is a set of strings that can be recognized by a finite-state automaton. In simple terms, a regular set is a set of strings that can be generated by a regular expression or accepted by a deterministic finite automaton (DFA).
Counterexample:
To disprove the statement, we need to find a counterexample where a subset of a regular set is not regular. Let's consider the following example:
Regular Set: L = {a^n b^n | n ≥ 0}
Subset: S = {ε, ab}
Explanation of the Example:
In the regular set L, every string consists of 'a's followed by the same number of 'b's. For example, "ab", "aabb", "aaabbb", etc., are all part of the regular set L.
Now, let's consider the subset S, which contains two strings: ε (empty string) and "ab". Both these strings are part of the regular set L.
However, the subset S is not regular because it violates the rule of having an equal number of 'a's and 'b's. The string "ab" does not have an equal number of 'a's and 'b's, which means it cannot be recognized by a finite-state automaton, and hence, it is not a regular set.
Conclusion:
The example above demonstrates that there exists a subset of a regular set (L) that is not regular (S). Therefore, the statement "Every subset of a regular set is regular" is false.
Explanation:
To understand why this statement is false, we need to have a clear understanding of what a regular set is.
Regular Set:
In formal language theory, a regular set is a set of strings that can be recognized by a finite-state automaton. In simple terms, a regular set is a set of strings that can be generated by a regular expression or accepted by a deterministic finite automaton (DFA).
Counterexample:
To disprove the statement, we need to find a counterexample where a subset of a regular set is not regular. Let's consider the following example:
Regular Set: L = {a^n b^n | n ≥ 0}
Subset: S = {ε, ab}
Explanation of the Example:
In the regular set L, every string consists of 'a's followed by the same number of 'b's. For example, "ab", "aabb", "aaabbb", etc., are all part of the regular set L.
Now, let's consider the subset S, which contains two strings: ε (empty string) and "ab". Both these strings are part of the regular set L.
However, the subset S is not regular because it violates the rule of having an equal number of 'a's and 'b's. The string "ab" does not have an equal number of 'a's and 'b's, which means it cannot be recognized by a finite-state automaton, and hence, it is not a regular set.
Conclusion:
The example above demonstrates that there exists a subset of a regular set (L) that is not regular (S). Therefore, the statement "Every subset of a regular set is regular" is false.
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
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Which of the following statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is regularCorrect answer is option 'B'. Can you explain this answer?
Question Description
Which of the following statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is regularCorrect answer is option 'B'. Can you explain this answer?.
Which of the following statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is regularCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is regularCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Which of the following statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is regularCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Which of the following statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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 statements is false?a)Every finite subset of a non-regular set is regularb)Every subset of a regular set is regularc)Every finite subset of a regular set is regulard)The intersection of two regular sets is 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup