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Consider the following set of statements:
S1: If L1 and L2 are regular languages, then L1 - L2 is also a regular language.
S2: Context free languages are closed under concatenation.
S3: Context free languages are closed under intersection.
S4: Regular language is closed under infinite union of regular languages.
Which of the given statements are true?
- a)Both S1 and S2
- b)Both S1 and S4
- c)Both S3 and S4
- d)Both S1 and S3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following set of statements:S1: If L1and L2are regular la...
Only statements S1 and S2 are true.
Context free languages are not closed under intersection. Also, regular languages are not closed under infinite union of regular languages.
Most Upvoted Answer
Consider the following set of statements:S1: If L1and L2are regular la...
Explanation:
S1: If L1 and L2 are regular languages, then L1-L2 is also a regular language.
This statement is true because regular languages are closed under complementation. L1-L2 is equivalent to the intersection of L1 and complement of L2, which is also a regular language.
S2: Context free languages are closed under concatenation.
This statement is true because if two context-free languages L1 and L2 are concatenated, the resulting language is also context-free. This can be proved using the closure property of context-free languages under concatenation.
S3: Context free languages are closed under intersection.
This statement is false because the intersection of two context-free languages is not necessarily context-free. This can be proved by giving an example of two context-free languages whose intersection is not context-free.
S4: Regular language is closed under infinite union of regular languages.
This statement is false because the infinite union of regular languages may not be regular. This can be proved by giving an example of two regular languages whose infinite union is not regular.
Therefore, the correct answer is option 'A' which states that both S1 and S2 are true.
S1: If L1 and L2 are regular languages, then L1-L2 is also a regular language.
This statement is true because regular languages are closed under complementation. L1-L2 is equivalent to the intersection of L1 and complement of L2, which is also a regular language.
S2: Context free languages are closed under concatenation.
This statement is true because if two context-free languages L1 and L2 are concatenated, the resulting language is also context-free. This can be proved using the closure property of context-free languages under concatenation.
S3: Context free languages are closed under intersection.
This statement is false because the intersection of two context-free languages is not necessarily context-free. This can be proved by giving an example of two context-free languages whose intersection is not context-free.
S4: Regular language is closed under infinite union of regular languages.
This statement is false because the infinite union of regular languages may not be regular. This can be proved by giving an example of two regular languages whose infinite union is not regular.
Therefore, the correct answer is option 'A' which states that both S1 and S2 are true.
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Consider the following set of statements:S1: If L1and L2are regular languages, then L1- L2is also a regular language.S2: Context free languages are closed under concatenation.S3: Context free languages are closed under intersection.S4: Regular language is closedunder infinite union of regular languages.Which of the given statements are true?a)Both S1and S2b)Both S1and S4c)Both S3and S4d)Both S1and S3Correct answer is option 'A'. Can you explain this answer?
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