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Consider the following languages: L1 = {ww | w ∈ {a,b}*} L2 = {a^m bⁿ c^m | m,n ≥ 0} L3 = {a^m bⁿ cⁿ | m,n ≥ 0} Which of the following statements is/are FALSE?

1. L1 is not context-free but L2 and L3 are deterministic context-free.
2. Neither L1 nor L2 is context-free.
3. L2, L3 and L2 ∩ L3 all are context-free.
4. Neither L1 nor its complement is context-free.

Correct answer: Neither L1 nor L2 is context-free.

Solution

The correct option states that neither L1 nor L2 is context-free, which is true because L1 requires matching strings that cannot be generated by a context-free grammar, and L2 requires a dependency between the number of 'a's and 'c's that also cannot be captured by context-free grammars.

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