Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following is TRUE?a)Every subset...
Start Learning for Free
Which of the following is TRUE?
- a)Every subset of a regular set is regular.
- b)Every finite subset of a non-regular set is regular.
- c)The union of two non-regular sets is not regular.
- d)Infinite union of finite 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 is TRUE?a)Every subset of a regular set is regu...
Some points for Regular Sets:
- A set is always regular if it is finite.
- A set is always regular if a DFA/NFA can be drawn for it.
Option A: Every subset of a regular set is regular is False. For input alphabets a and b, a*b* is regular. A DFA can be drawn for a*b* but a n b n for n≥0 which is a subset of a*b* is not regular as we cannot define a DFA for it.
Option B: Every finite subset of a non-regular set is regular is True. Each and every set which is finite can have a well-defined DFA for it so whether it is a subset of a regular set or non-regular set it is always regular.
Option C: The union of two non-regular sets is not regular is False. For input alphabets a and b, an bn for all n≥0 is non-regular as well as an bm for n≠m is also non- regular but their union is a*b* which is regular.
Option D: TInfinite union of finite sets is regular is False. For input alphabets a and b sets {ab}, {aabb}, {aaabbb}…….. are regular but their union {ab} U {aabb} U {aaabbb} U …………………….. gives {a n b n for n>0} which is not regular.
Option B: Every finite subset of a non-regular set is regular is True. Each and every set which is finite can have a well-defined DFA for it so whether it is a subset of a regular set or non-regular set it is always regular.
Option C: The union of two non-regular sets is not regular is False. For input alphabets a and b, an bn for all n≥0 is non-regular as well as an bm for n≠m is also non- regular but their union is a*b* which is regular.
Option D: TInfinite union of finite sets is regular is False. For input alphabets a and b sets {ab}, {aabb}, {aaabbb}…….. are regular but their union {ab} U {aabb} U {aaabbb} U …………………….. gives {a n b n for n>0} which is not regular.
Most Upvoted Answer
Which of the following is TRUE?a)Every subset of a regular set is regu...
Explanation:
Regular Set: A set that can be recognized by a finite automaton is called a regular set.
Non-Regular Set: A set that cannot be recognized by a finite automaton is called a non-regular set.
a) Every subset of a regular set is regular: This statement is true. Suppose we have a regular set R and a subset of R called S. Since R is regular, it can be recognized by a finite automaton. Since S is a subset of R, any string that is in S must also be in R. Therefore, S can also be recognized by the same finite automaton that recognizes R, and hence S is also regular.
b) Every finite subset of a non-regular set is regular: This statement is true. Suppose we have a non-regular set N and a finite subset of N called F. Since N is non-regular, it cannot be recognized by any finite automaton. However, F is a finite set, and therefore, we can list all the strings in F. We can then construct a finite automaton that recognizes all the strings in F, which means that F is regular.
c) The union of two non-regular sets is not regular: This statement is false. There exist non-regular sets whose union is regular. For example, let A be the set of all strings of the form 0^n1^n (where n is a positive integer), and let B be the set of all strings of the form 1^n0^n. Both A and B are non-regular sets, but their union (which is the set of all strings of the form 0^n1^n or 1^n0^n) is regular.
d) Infinite union of finite sets is regular: This statement is false. There exist infinite unions of finite sets that are non-regular. For example, let A_n be the set of all strings of length n over the alphabet {0, 1}. Each A_n is a finite set, but their infinite union (which is the set of all binary strings) is non-regular. This can be proved using the pumping lemma for regular sets.
Regular Set: A set that can be recognized by a finite automaton is called a regular set.
Non-Regular Set: A set that cannot be recognized by a finite automaton is called a non-regular set.
a) Every subset of a regular set is regular: This statement is true. Suppose we have a regular set R and a subset of R called S. Since R is regular, it can be recognized by a finite automaton. Since S is a subset of R, any string that is in S must also be in R. Therefore, S can also be recognized by the same finite automaton that recognizes R, and hence S is also regular.
b) Every finite subset of a non-regular set is regular: This statement is true. Suppose we have a non-regular set N and a finite subset of N called F. Since N is non-regular, it cannot be recognized by any finite automaton. However, F is a finite set, and therefore, we can list all the strings in F. We can then construct a finite automaton that recognizes all the strings in F, which means that F is regular.
c) The union of two non-regular sets is not regular: This statement is false. There exist non-regular sets whose union is regular. For example, let A be the set of all strings of the form 0^n1^n (where n is a positive integer), and let B be the set of all strings of the form 1^n0^n. Both A and B are non-regular sets, but their union (which is the set of all strings of the form 0^n1^n or 1^n0^n) is regular.
d) Infinite union of finite sets is regular: This statement is false. There exist infinite unions of finite sets that are non-regular. For example, let A_n be the set of all strings of length n over the alphabet {0, 1}. Each A_n is a finite set, but their infinite union (which is the set of all binary strings) is non-regular. This can be proved using the pumping lemma for regular sets.
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 is TRUE?a)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct answer is option 'B'. Can you explain this answer?
Question Description
Which of the following is TRUE?a)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct answer is option 'B'. Can you explain this answer?.
Which of the following is TRUE?a)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct answer is option 'B'. Can you explain this answer?.
Solutions for Which of the following is TRUE?a)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Which of the following is TRUE?a)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Which of the following is TRUE?a)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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)Every subset of a regular set is regular.b)Every finite subset of a non-regular set is regular.c)The union of two non-regular sets is not regular.d)Infinite union of finite sets is regular.Correct 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