Correct Answer - Option 2 : Complementation
Concept:
Context free languages are closed under Union, Concatenation and Kleene Closure (star)
CFLs are NOT closed under intersection and not closed under complementation
Example:
L1 = pn qn rm | m, n > 0 → CFL
L2 = pm qn rn | m, n > 0 → CFL
L = pn qn rm ∩ pm qn rn | m, n > 0. L = pn qn rn it is not accepted by pushdown automaton and hence it is not a CFL. and hence it is not closed under intersection.
Important Point:
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Context free languages
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Only Deterministic Context free languages
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Closed under
- Union
- Concatenation
- Kleene Closure
- Homomorphism
- Inverse Homomorphism
- Reversal of language
- Intersection with Regular language
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Closed under
- Complementation
- Inverse Homomorphism
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Not Closed under
- Complementation
- Intersection
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Not Closed under
- Union
- Intersection
- Concatenation
- Kleene closure
- Homomorphism
- Reversal of language
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