Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following statements.I. If L1&cu...
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Consider the following statements.
I. If L1 ∪ L2 is regular, then both L1 and L2 must be regular.
II. The class of regular languages is closed under infinite union.
Which of the above statements is/are TRUE?
- a)I only
- b)II only
- c)Both I and II
- d)Neither I nor II
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider the following statements.I. If L1∪ L2is regular, then bot...
Statement I: FALSE
If L1 ∪ L2 is regular, then neither L1 nor L2 needs necessarily be regular.
Example:
Assume L1= {an bn, n ≥ 0} over the alphabet {a, b} and L2 be the complement of L1.
Neither L1 nor L2 is regular (both are DCFL) but L1 ∪ L2= {an bn} ∪ {an bn}c = (a + b)* is regular.
Statement II: FALSE. The infinite Union of regular languages is not regular.
Example:
Given alphabet {a, b}.
L1= {ε}
L2= {ab}
L3= {aabb}
L4= {aaabbb}
:
:
L = L1 ∪ L2 ∪ L3 ∪ L4 …
Each of the above are regular but their infinite Union gives L1= {an bn, n ≥ 0} which is not regular but DCFL.
Note:
DCFL → Deterministic context free language
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Community Answer
Consider the following statements.I. If L1∪ L2is regular, then bot...
Is true, then L2 is true.
II. If L2 is true, then L3 is true.
III. If L3 is true, then L4 is true.
IV. If L4 is true, then L5 is true.
Which of the following conclusions can be drawn from the above statements?
A. If L5 is true, then L4 is true.
B. If L4 is true, then L3 is true.
C. If L3 is true, then L2 is true.
D. If L2 is true, then L1 is true.
E. If L1 is true, then L5 is true.
II. If L2 is true, then L3 is true.
III. If L3 is true, then L4 is true.
IV. If L4 is true, then L5 is true.
Which of the following conclusions can be drawn from the above statements?
A. If L5 is true, then L4 is true.
B. If L4 is true, then L3 is true.
C. If L3 is true, then L2 is true.
D. If L2 is true, then L1 is true.
E. If L1 is true, then L5 is true.
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Consider the following statements.I. If L1∪ L2is regular, then both L1and L2must be regular.II. The class of regular languages is closed under infinite union.Which of the above statements is/are TRUE?a)I onlyb)II onlyc)Both I and IId)Neither I nor IICorrect answer is option 'D'. Can you explain this answer?
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