Let L1 is CFL, L2 is DCFL and L3 is regular. Then (L1 ∪ (L2 ∩ (L̅3)))
(A) Regular
(B) DCFL but not regular
(C) CFL but not DCFL
(D) CSL but not CFL
Answer: (C)
Explanation: (L1 ∪ (L2 ∩ (L̅3)))
Complement of regular language is regular.
(L1 ∪ (L2 ∩ (Regular)))
Intersection of a regular language and DCFL is DCFL
(L1 ∪ DCFL)
Now Union push DCFL to CFL
And we know that union of two CFL language is CFL.
So, option (C) is correct.
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