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GATE CSE 2005 | Question: 55

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Consider the languages:

$L_1 = \left\{ a^nb^nc^m \mid n,m >0\right\}$  and $ L_2 = \left\{a^nb^mc^m\mid n, m > 0\right\}$

Which one of the following statements is FALSE?

  1. $L_1 \cap L_2$ is a context-free language

  2. $L_1 \cup L_2$ is a context-free language

  3. $L_1 \text{ and } L_2$ are context-free languages

  4. $L_1 \cap L_2$ is a context sensitive language

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6 Answers

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If  $L1∩L2$  is a context-free language then it must also be Context Sensitive language

as $CFL ⊂ CSL$

then A must be false

apart from best selected answer you can pick up this point too

answer Option A
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