Q38

MSQ2 marks

Consider the following languages: $L_{1} = \{ ww | w \in \{a,b\}^{\ast} \}$ $L_{2} = \{a^{n} b^{n} c^{m} | m,n \geq 0 \}$ $L_{3} = \{a^{m} b^{n} c^{n} | m,n \geq 0 \}$ Which of the following statements is/are $\text{FALSE}?$

(A)

$L_{1}$ is not context-free but $L_{2}$ and $L_{3}$ are deterministic context-free.

(B)

Neither $L_{1}$ nor $L_{2}$ is context-free.

(C)

$L_{2}, L_{3}$ and $L_{2} \cap L_{3}$ all are context-free.

(D)

Neither $L_{1}$ nor its complement is context-free.

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