Using the property that the intersection of a CFL and a regular language is still a CFL, and the fact that the language 0 ≤ m ≤ n is not context free, prove that the following …

Question

Using the property that the intersection of a CFL and a regular language is still a CFL, and the fact that the language

a^n b^n c^m is not context free, prove that the following language A is not context free.
A = w ∈ Σ∗, and in w, the number of a’s is equal to the number of b’s and is larger than or equal to the number of c’s,
(i.e., aabcb and cba are in A. baac or accb are not in A.)

Answer 1

To prove that the language A is not context-free, we can use the intersection property with a non-context-free language and a regular language.

Step-by-step explanation:

To prove that the language A = w ∈ Σ∗, and in w, the number of a’s is equal to the number of b’s and is larger than or equal to the number of c’s is not context-free, we can use the fact that the language a^n b^n c^m is not context-free. We can create an intersection between this non-context-free language and a regular language to show that A is not context-free. By proving that the resulting language is not context-free, we can conclude that A is also not context-free.

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