Gate2020 cs Q17

17Consider the language L = {aⁿ| n ≥ 0} ∪ { aⁿbⁿ | n ≥ 0} and the following statements.
I. L is deterministic context-free.
II. L is context-free but not deterministic context-free.
III. L is not LL(k) for any k.
Which of the above statements is/are TRUE?

Option : B
Explanation :
Statement I - L = {aⁿ| n ≥ 0} ∪ { aⁿbⁿ | n ≥ 0}
↓ ↓
Linear power well know DCFL
∴ it is regular
∴ L = Regular ∪ DCFL {use the closure properties}
L = DCLF
Statement--III As we cannot write LL( k ) grammar, for any value of k, Hence statement III is correct.

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