# Find context-free grammars for the following languages (with n ≥ 0, m ≥ 0, k ≥ 0):  L = {anbmck, k = n + m}.

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Find context-free grammars for the following languages (with n ≥ 0, m ≥ 0, k ≥ 0):  L = {anbmckk = n + m}.

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Step 1

Solution:

Given language,

L = {anbmck, k = n+m}

Consider the “G” as grammar production is given below:

Step 2

Here, we need to prove that L(G) = L

To attain above expression, we need to prove that “L is subset of L(G)” and “L(G) is subset of L”.

Derive the string “S” by following methods:

From the given language L, S can be derived as

Step 3

The “S-> anbmc(m+n)” statement consider as equation (1).

Here, the primary thing is to apply “*” to “S” with for string for “n” tim...

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### Automated Reasoning 