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Context-free languages are closed under:

1. Union, intersection

2. Union, Kleene closure

3. Intersection, complement

4. Complement, Kleene closure

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Context free languages are not closed under intersection and complement. Correct option is (B) Union and Kleene closure.

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Arjun sir, please tell is it the case that DCFL* is CSL always?
No. Consider $L_1 = \{a^nb^n\} \cup \{ca^nb^{2n}\}$. Let $L = \{c\} \cup L_1$. L is DCFL. But L* is CFL
This came in TIFR

The context-free languages are closed under union, concatenation and Kleene closure.

so option B

by
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CFLs are not closed under intersection, complement and set difference. Hence, the correct option is (B).
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ankit, is DCFL* is CSL?
edited
DCFL are not closed under Kleene closure, which means it may or may not be DCFL. So, we can't really comment about whether it would bs CSL or not. Hence, not a CSL. Please correct me if I'm wrong.

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