Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following two statements:I. If a...
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Consider the following two statements:
I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ∗ .
II. There exists a regular language A such that for all languages B, A ∩ B is regular.
II. There exists a regular language A such that for all languages B, A ∩ B is regular.
Q. Which one of the following is CORRECT?
- a)Only I is true
- b)Only II is true
- c)Both I and II are true
- d)Both I and II are false
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider the following two statements:I. If all states of an NFA are a...
Statement I : False, Since there is no mention of transition between states. There may be a case, where between two states there is no transition defined.
Statement II: True, Since any empty language (i.e., A = Φ ) is regular and its intersection with any other language is Φ. Thus A ∩ B is regular.
Statement II: True, Since any empty language (i.e., A = Φ ) is regular and its intersection with any other language is Φ. Thus A ∩ B is regular.
Most Upvoted Answer
Consider the following two statements:I. If all states of an NFA are a...
Explanation:
Statement I:
- The statement is false. If all states of an NFA are accepting states, it does not guarantee that the language accepted by the NFA is empty. There can be transitions leading to non-accepting states as well, thus making the language non-empty.
Statement II:
- The statement is true. There exists a regular language A (e.g., the empty set) such that for all languages B, A ∩ B is regular. The intersection of a regular language with any language results in a regular language. This property demonstrates that regular languages are closed under intersection.
Therefore, the correct answer is option 'B' - Only II is true.
Statement I:
- The statement is false. If all states of an NFA are accepting states, it does not guarantee that the language accepted by the NFA is empty. There can be transitions leading to non-accepting states as well, thus making the language non-empty.
Statement II:
- The statement is true. There exists a regular language A (e.g., the empty set) such that for all languages B, A ∩ B is regular. The intersection of a regular language with any language results in a regular language. This property demonstrates that regular languages are closed under intersection.
Therefore, the correct answer is option 'B' - Only II is true.
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Consider the following two statements:I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ∗ .II. There exists a regular language A such that for all languages B, A ∩ B is regular.Q.Which one of the following is CORRECT?a)Only I is trueb)Only II is truec)Both I and II are trued)Both I and II are falseCorrect answer is option 'B'. Can you explain this answer?
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