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Consider the languages
L1 = { an bn cm | n , m > 0 } and L2 = { an bm cm | n , m > 0 }
Which one of the following statements is false?
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- L1 ∩ L2 is a context-free language
- L1 ∪ L2 is a context-free language
- L1 and L2 are context-free language
- L1 ∩ L2 is a context-sensitive language
- L1 ∩ L2 is a context-free language
Correct Option: A
L1 and L2 are context-free languages and therefore L1 ∩ L2 may or may not be context-free, since CFLs are not closed under intersection. Now, let us look at L1 ∩ L2 .
L1 ∩ L2 = { an bn cn | n > 0 }
which is clearly not context-free but is context sensitive.
